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ETA FUNCTION

  • Dirichlet eta function
  • Function in analytic number theory

    In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any

    Dirichlet eta function

    Dirichlet eta function

    Dirichlet_eta_function

  • Dedekind eta function
  • Mathematical function

    In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane

    Dedekind eta function

    Dedekind_eta_function

  • Eta function
  • Topics referred to by the same term

    eta function may refer to: The Dirichlet eta function η(s), a Dirichlet series The Dedekind eta function η(τ), a modular form The Weierstrass eta function

    Eta function

    Eta_function

  • Eta
  • Seventh letter in the Greek alphabet

    Eta (/ˈiːtə, ˈeɪtə/ EE-tə, AY-tə; uppercase Η, lowercase η; Ancient Greek: ἦτα ē̂ta [ɛ̂ːta] or Greek: ήτα ita [ˈita]) is the seventh letter of the Greek

    Eta

    Eta

  • Weierstrass functions
  • Mathematical functions related to Weierstrass's elliptic function

    Weierstrass eta function should not be confused with either the Dedekind eta function or the Dirichlet eta function. The Weierstrass p-function is related

    Weierstrass functions

    Weierstrass_functions

  • Fubini's theorem
  • Conditions for switching order of integration in calculus

    Dirichlet eta function as follows: η ( s ) = ∑ n = 1 ∞ ( − 1 ) n − 1 n s = 1 − 1 2 s + 1 3 s − 1 4 s + 1 5 s − 1 6 s ± ⋯ {\displaystyle \eta (s)=\sum _{n=1}^{\infty

    Fubini's theorem

    Fubini's_theorem

  • Rogers–Ramanujan identities
  • Mathematical identities related to integer partitions

    eta function in their Weber form: G M ( q ) = η W ( q 5 ) 1 / 2 η W ( q ) − 1 / 2 R ( q ) − 1 / 2 {\displaystyle G_{M}(q)=\eta _{W}(q^{5})^{1/2}\eta

    Rogers–Ramanujan identities

    Rogers–Ramanujan_identities

  • Eta (disambiguation)
  • Topics referred to by the same term

    Look up eta or ETA in Wiktionary, the free dictionary. Eta (Η or η) is the seventh letter of the Greek alphabet. Eta or ETA may also refer to: Eta (given

    Eta (disambiguation)

    Eta_(disambiguation)

  • Theta function
  • Special functions of several complex variables

    1 , {\displaystyle \tau =n{\sqrt {-1}},} and Dedekind eta function η ( τ ) . {\displaystyle \eta (\tau ).} Then for n = 1 , 2 , 3 , … {\displaystyle n=1

    Theta function

    Theta function

    Theta_function

  • Riemann zeta function
  • Analytic function in mathematics

    physics. 1 + 2 + 3 + 4 + ··· Arithmetic zeta function Apéry's constant Basel problem Dirichlet eta function Generalized Riemann hypothesis Lehmer pair Particular

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • List of mathematical functions
  • Synchrotron function Riemann zeta function: A special case of Dirichlet series. Riemann Xi function Dirichlet eta function: An allied function. Dirichlet

    List of mathematical functions

    List_of_mathematical_functions

  • Ramanujan tau function
  • Function studied by Ramanujan

    (q)^{24}=\eta (z)^{24}=\Delta (z),} where ϕ {\displaystyle \phi } is the Euler function, η {\displaystyle \eta } is the Dedekind eta function, Δ ( z )

    Ramanujan tau function

    Ramanujan tau function

    Ramanujan_tau_function

  • Chowla–Selberg formula
  • Evaluates a certain product of values of the Gamma function at rational values

    certain product of values of the gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers

    Chowla–Selberg formula

    Chowla–Selberg_formula

  • Ramanujan–Sato series
  • Series related to Ramanujan's pi formulas

    \end{aligned}}} with the j-function j(τ), Eisenstein series E4, and Dedekind eta function η(τ). The first expansion is the McKay–Thompson

    Ramanujan–Sato series

    Ramanujan–Sato_series

  • 24 (number)
  • Natural number

    modular forms through the Dedekind eta function η ( τ ) = q 1 / 24 ∏ n > 0 ( 1 − q n ) , q = e 2 π i τ . {\displaystyle \eta (\tau )=q^{1/24}\prod _{n>0}(1-q^{n})

    24 (number)

    24_(number)

  • 1 + 2 + 3 + 4 + ⋯
  • Divergent series

    uses the relationship between the Riemann zeta function and the Dirichlet eta function η(s). The eta function is defined by an alternating Dirichlet series

    1 + 2 + 3 + 4 + ⋯

    1 + 2 + 3 + 4 + ⋯

    1_+_2_+_3_+_4_+_⋯

  • Kronecker limit formula
  • Mathematical theorem about the real analytic Eisenstein series

    a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more complicated

    Kronecker limit formula

    Kronecker_limit_formula

  • Dirac delta function
  • Generalized function whose value is zero everywhere except at zero

    \eta _{\varepsilon }*\eta _{\delta }=\eta _{\varepsilon +\delta }} for all ε, δ > 0. Convolution semigroups in L1 that approximate the delta function are

    Dirac delta function

    Dirac delta function

    Dirac_delta_function

  • Partition function (number theory)
  • Number of partitions of an integer

    specifically the Dedekind eta function. The same sequence of pentagonal numbers appears in a recurrence relation for the partition function: p ( n ) = ∑ k ∈ Z

    Partition function (number theory)

    Partition function (number theory)

    Partition_function_(number_theory)

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    this continuation observes that the series for the zeta function and the Dirichlet eta function satisfy the relation ( 1 − 2 2 s ) ζ ( s ) = η ( s ) =

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • J-invariant
  • Modular function in mathematics

    )^{3}-27g_{3}(\tau )^{2}=(2\pi )^{12}\,\eta (\tau )^{24}} , Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} , and modular invariants, g 2 (

    J-invariant

    J-invariant

    J-invariant

  • Euler function
  • Mathematical function

    {\displaystyle (3n^{2}-n)/2} is a pentagonal number. The Euler function is related to the Dedekind eta function as ϕ ( e 2 π i τ ) = e − π i τ / 12 η ( τ ) . {\displaystyle

    Euler function

    Euler function

    Euler_function

  • Eta invariant
  • Differential operator

    generalization of the Dirichlet eta function. They also later used the eta invariant of a self-adjoint operator to define the eta invariant of a compact odd-dimensional

    Eta invariant

    Eta_invariant

  • Modular lambda function
  • Symmetric holomorphic function

    )=k^{2}(\tau )} . In terms of the Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} and theta functions, λ ( τ ) = ( 2 η ( τ 2 ) η 2 ( 2 τ ) η 3

    Modular lambda function

    Modular lambda function

    Modular_lambda_function

  • Weber modular function
  • \eta (2\tau )}{\eta (\tau )}}.\end{aligned}}} These are also the definitions in Duke's paper "Continued Fractions and Modular Functions". The function

    Weber modular function

    Weber_modular_function

  • Polylogarithm
  • Special mathematical function

    to Dirichlet eta function and the Dirichlet beta function: Li s ⁡ ( − 1 ) = − η ( s ) , {\displaystyle \operatorname {Li} _{s}(-1)=-\eta (s),} where η(s)

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Modular form
  • Analytic function on the upper half-plane with a certain behavior under the modular group

    discriminant The Dedekind eta function is defined as η ( z ) = q 1 / 24 ∏ n = 1 ∞ ( 1 − q n ) , q = e 2 π i z . {\displaystyle \eta (z)=q^{1/24}\prod _{n=1}^{\infty

    Modular form

    Modular_form

  • Greek letters used in mathematics, science, and engineering
  • Symbols for constants, special functions

    Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics Information theoretic (Shannon) entropy η {\displaystyle \eta }

    Greek letters used in mathematics, science, and engineering

    Greek_letters_used_in_mathematics,_science,_and_engineering

  • 12 (number)
  • Natural number

    Ramanujan τ {\displaystyle \tau } -function and which is (up to a constant multiplier) the 24th power of the Dedekind eta function: Δ ( τ ) = ( 2 π ) 12 η 24

    12 (number)

    12_(number)

  • ETA (separatist group)
  • Basque separatist group (1960–2018)

    ETA, an acronym for Euskadi Ta Askatasuna ('Basque Homeland and Liberty' or 'Basque Country and Freedom' in Basque), was an armed Basque nationalist and

    ETA (separatist group)

    ETA (separatist group)

    ETA_(separatist_group)

  • Dedekind function
  • Topics referred to by the same term

    function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta function This

    Dedekind function

    Dedekind_function

  • Weierstrass elliptic function
  • Class of mathematical functions

    24 {\displaystyle \Delta =(2\pi )^{12}\eta ^{24}} where η {\displaystyle \eta } is the Dedekind eta function. For the Fourier coefficients of Δ {\displaystyle

    Weierstrass elliptic function

    Weierstrass elliptic function

    Weierstrass_elliptic_function

  • Zolotarev polynomials
  • Polynomials used in approximation theory

    height as the equiripple peaks. The Jacobi eta function can be defined in terms of a Jacobi auxiliary theta function, H ( φ | κ ) = θ 1 ( a | b ) {\displaystyle

    Zolotarev polynomials

    Zolotarev_polynomials

  • Ramanujan theta function
  • Mathematical function

    Euler function, which is closely related to the Dedekind eta function. The Jacobi theta function may be written in terms of the Ramanujan theta function as:

    Ramanujan theta function

    Ramanujan_theta_function

  • 1 − 2 + 3 − 4 + ⋯
  • Infinite series with alternating signs

    functional equations of what are now known as the Dirichlet eta function and the Riemann zeta function. The series' terms (1, −2, 3, −4, ...) do not approach

    1 − 2 + 3 − 4 + ⋯

    1 − 2 + 3 − 4 + ⋯

    1_−_2_+_3_−_4_+_⋯

  • Optical resolution
  • Ability of an imaging system to resolve detail

    \operatorname {sinc} (\xi ,\eta )} function corresponding to the active area. That last function serves as an overall envelope to the MTF function; so long as the

    Optical resolution

    Optical_resolution

  • Clausen function
  • Transcendental single-variable function

    tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred

    Clausen function

    Clausen function

    Clausen_function

  • Shimizu L-function
  • signature defect of the boundary of a manifold as the eta invariant, the value as s=0 of their eta function, and used this to show that Hirzebruch's signature

    Shimizu L-function

    Shimizu_L-function

  • Isoelastic utility
  • Concept in economics

    η {\displaystyle \eta } is a constant that is positive for risk averse agents. Since additive constant terms in objective functions do not affect optimal

    Isoelastic utility

    Isoelastic utility

    Isoelastic_utility

  • Eta Carinae
  • Stellar system in the constellation Carina

    Eta Carinae (η Carinae, abbreviated to η Car), formerly known as η Argus, is a stellar system containing at least two stars with a combined luminosity

    Eta Carinae

    Eta Carinae

    Eta_Carinae

  • Automorphic form
  • Type of generalization of periodic functions in Euclidean space

    harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G {\displaystyle G} to the complex numbers (or

    Automorphic form

    Automorphic_form

  • Matsubara summation
  • Mathematical technique in thermal field theory

    S_{\eta }={\frac {1}{\beta }}\sum _{i\omega }g(i\omega )={\frac {1}{2\pi i\beta }}\oint g(z)h_{\eta }(z)\,dz,} As in Fig. 1, the weighting function generates

    Matsubara summation

    Matsubara_summation

  • Exponential family
  • Family of probability distributions related to the normal distribution

    \right)}=h(x)\,\exp \left[\eta (\theta )\cdot T(x)-A(\theta )\right]} where T(x), h(x), η(θ), and A(θ) are known functions. The function h(x) must be non-negative

    Exponential family

    Exponential_family

  • Dedekind sum
  • products of a sawtooth function. Dedekind introduced them in the 1880's to express the functional equation of the Dedekind eta function, in a commentary to

    Dedekind sum

    Dedekind_sum

  • Srinivasa Ramanujan
  • Indian mathematician (1887–1920)

    (\theta )|<\pi } , where Γ(z) is the gamma function, and related to a special value of the Dedekind eta function. Expanding into series of powers and equating

    Srinivasa Ramanujan

    Srinivasa Ramanujan

    Srinivasa_Ramanujan

  • Invex function
  • vector valued function η {\displaystyle \eta } such that f ( x ) − f ( u ) ≥ η ( x , u ) ⋅ ∇ f ( u ) , {\displaystyle f(x)-f(u)\geq \eta (x,u)\cdot \nabla

    Invex function

    Invex_function

  • Analytic function of a matrix
  • Function that maps matrices to matrices

    {\begin{aligned}f(a+\eta b)&=f(a)+f'(a){\frac {\eta b}{1!}}+f''(a){\frac {(\eta b)^{2}}{2!}}+f'''(a){\frac {(\eta b)^{3}}{3!}}\\[.5em]&=a^{3}+3a^{2}(\eta b)+3a(\eta b)^{2}+(\eta

    Analytic function of a matrix

    Analytic_function_of_a_matrix

  • Rogers–Ramanujan continued fraction
  • Continued fraction closely related to the Rogers–Ramanujan identities

    throughout this section since the q-expansion of the j-function (as well as the well-known Dedekind eta function) uses q = e 2 π i τ {\displaystyle q=e^{2\pi i\tau

    Rogers–Ramanujan continued fraction

    Rogers–Ramanujan continued fraction

    Rogers–Ramanujan_continued_fraction

  • Loss functions for classification
  • Concept in machine learning

    {\displaystyle C(\eta )} is any differentiable strictly concave function such that C ( η ) = C ( 1 − η ) {\displaystyle C(\eta )=C(1-\eta )} . Table-I shows

    Loss functions for classification

    Loss functions for classification

    Loss_functions_for_classification

  • Coulomb wave function
  • In physics, solution to Schrödinger equation

    hypergeometric function, η = Z m c α / ( ℏ k ) {\displaystyle \eta =Zmc\alpha /(\hbar k)} and Γ ( z ) {\displaystyle \Gamma (z)} is the gamma function. The two

    Coulomb wave function

    Coulomb wave function

    Coulomb_wave_function

  • Lambda calculus
  • Mathematical-logic system based on functions

    POW′′ := λb.λn.λf.n b f but that is just an eta-expanded version of POW we already have, above. The predecessor function, specified by two equations PRED (SUCC

    Lambda calculus

    Lambda calculus

    Lambda_calculus

  • Fischer group Fi22
  • Sporadic simple group

    {\eta (\tau )\,\eta (3\tau )}{\eta (2\tau )\,\eta (6\tau )}}\right)^{3}+2^{3}\left({\tfrac {\eta (2\tau )\,\eta (6\tau )}{\eta (\tau )\,\eta (3\tau

    Fischer group Fi22

    Fischer group Fi22

    Fischer_group_Fi22

  • Gradient descent
  • Optimization algorithm

    sequence η n {\displaystyle \eta _{n}} satisfying the Wolfe conditions (which can be found by using line search). When the function f {\displaystyle f} is convex

    Gradient descent

    Gradient descent

    Gradient_descent

  • Wallis product
  • Infinite product for pi

    {\displaystyle k\rightarrow \infty } . The Riemann zeta function and the Dirichlet eta function can be defined: ζ ( s ) = ∑ n = 1 ∞ 1 n s , ℜ ( s ) > 1

    Wallis product

    Wallis product

    Wallis_product

  • Likelihood function
  • Function related to statistics and probability theory

    {\boldsymbol {\eta }}} ⁠ and the sufficient statistic ⁠ T ( x ) {\displaystyle \mathbf {T} (x)} ⁠, minus the normalization factor (log-partition function) ⁠ A (

    Likelihood function

    Likelihood_function

  • Dirichlet beta function
  • Special mathematical function

    last identity was derived by Malmsten in 1842. Hurwitz zeta function Dirichlet eta function Polylogarithm Dirichlet Beta – Hurwitz zeta relation, Engineering

    Dirichlet beta function

    Dirichlet beta function

    Dirichlet_beta_function

  • Spt function
  • z ) {\displaystyle \eta (z)} denote the Dedekind eta function. Then for q = e 2 π i z {\displaystyle q=e^{2\pi iz}} , the function S ~ ( z ) := q − 1 /

    Spt function

    Spt_function

  • Edmund Landau
  • German mathematician (1877–1938)

    inequality Landau–Ramanujan constant Landau's problem on the Dirichlet eta function Landau kernel Endmund Landau (1895). "Zur relativen Wertbemessung der

    Edmund Landau

    Edmund Landau

    Edmund_Landau

  • Heegner number
  • Concept in algebraic number theory

    cubics can be exactly given by quotients of the Dedekind eta function η(τ), a modular function involving a 24th root, and which explains the 24 in the

    Heegner number

    Heegner_number

  • Prolate spheroidal wave function
  • Special type of functions in mathematics

    {\displaystyle S_{mn}(c,\eta )=(1-\eta ^{2})^{m/2}Y_{mn}(c,\eta )} , the function Y m n ( c , η ) {\displaystyle Y_{mn}(c,\eta )} satisfies   ( 1 − η 2

    Prolate spheroidal wave function

    Prolate_spheroidal_wave_function

  • Gompertz distribution
  • Continuous probability distribution, named after Benjamin Gompertz

    function of the Gompertz distribution is: f ( x ; η , b ) = b η exp ⁡ ( η + b x − η e b x ) for  x ≥ 0 , {\displaystyle f\left(x;\eta ,b\right)=b\eta

    Gompertz distribution

    Gompertz distribution

    Gompertz_distribution

  • Partition function (quantum field theory)
  • Generating function for quantum correlation functions

    Grassmann currents η {\displaystyle \eta } and η ¯ {\displaystyle {\bar {\eta }}} so that the partition function is Z [ η ¯ , η ] = ∫ D ψ ¯ D ψ   e i

    Partition function (quantum field theory)

    Partition function (quantum field theory)

    Partition_function_(quantum_field_theory)

  • Generalized linear model
  • Class of statistical models

    distributions, 2. A linear predictor η = X β {\displaystyle \eta =X\beta } , and 3. A link function g {\displaystyle g} such that E ⁡ ( Y ∣ X ) = μ = g − 1

    Generalized linear model

    Generalized_linear_model

  • Cusp form
  • the Dedekind eta function. The Fourier coefficients here are written τ ( n ) {\displaystyle \tau (n)} and called 'Ramanujan's tau function', with the normalization

    Cusp form

    Cusp_form

  • Harada–Norton group
  • Sporadic simple group

    12256q^{4}+39350q^{5}+\dots \end{aligned}}} and η(τ) is the Dedekind eta function. Norton & Wilson (1986) found the 14 conjugacy classes of maximal subgroups

    Harada–Norton group

    Harada–Norton group

    Harada–Norton_group

  • Richard Dedekind
  • German mathematician (1831–1916)

    Dedekind domain Dedekind eta function Dedekind-infinite set Dedekind number Dedekind psi function Dedekind sum Dedekind zeta function Ideal (ring theory) "Dedekind"

    Richard Dedekind

    Richard Dedekind

    Richard_Dedekind

  • Euler–Lagrange equation
  • Second-order partial differential equation describing motion of mechanical system

    small and η {\displaystyle \eta } is a differentiable function satisfying η ( a ) = η ( b ) = 0 {\displaystyle \eta (a)=\eta (b)=0} . Then define Φ ( ε

    Euler–Lagrange equation

    Euler–Lagrange_equation

  • D'Alembert operator
  • Second-order differential operator

    {\displaystyle \eta _{00}=1} , η 11 = η 22 = η 33 = − 1 {\displaystyle \eta _{11}=\eta _{22}=\eta _{33}=-1} , η μ ν = 0 {\displaystyle \eta _{\mu \nu }=0}

    D'Alembert operator

    D'Alembert_operator

  • Elliptic curve
  • Algebraic curve in mathematics

    )^{2}=(2\pi )^{12}\,\eta ^{24}(\tau )} is generally a transcendental number. In particular, the value of the Dedekind eta function η(2i) is η ( 2 i ) =

    Elliptic curve

    Elliptic curve

    Elliptic_curve

  • Voigt profile
  • Probability distribution

    {\displaystyle V_{p}(x,f)=\eta \cdot L(x,f)+(1-\eta )\cdot G(x,f)} with 0 < η < 1 {\displaystyle 0<\eta <1} . η {\displaystyle \eta } is a function of full width at

    Voigt profile

    Voigt profile

    Voigt_profile

  • Baby monster group
  • Sporadic simple group

    2q^{3}+10698752q^{4}+\cdots \end{aligned}}} and η(τ) is the Dedekind eta function. Wilson (1999) found the 30 conjugacy classes of maximal subgroups of

    Baby monster group

    Baby monster group

    Baby_monster_group

  • Bosonic string theory
  • 26-dimensional string theory

    _{1}<{\frac {1}{2}}\right\}} . η ( τ ) {\displaystyle \eta (\tau )} is the Dedekind eta function. The integrand is of course invariant under the modular

    Bosonic string theory

    Bosonic_string_theory

  • Shifted Gompertz distribution
  • Probability distribution

    {\displaystyle \eta } . It is more flexible than the Gumbel distribution. The hazard rate is a concave function of F ( x ; b , η ) {\displaystyle F(x;b,\eta )} which

    Shifted Gompertz distribution

    Shifted Gompertz distribution

    Shifted_Gompertz_distribution

  • Complete Fermi–Dirac integral
  • Mathematical integral

    {\displaystyle F_{j}(0)=\eta (j+1),} where η {\displaystyle \eta } is the Dirichlet eta function. Incomplete Fermi–Dirac integral Gamma function Polylogarithm Gradshteyn

    Complete Fermi–Dirac integral

    Complete_Fermi–Dirac_integral

  • Signature defect
  • signature defect of the boundary of a manifold as the eta invariant, the value as s = 0 of their eta function, and used this to show that Hirzebruch's signature

    Signature defect

    Signature_defect

  • Blasius boundary layer
  • Two-dimensional laminar boundary layer that forms on a semi-infinite plate

    stream function. The stream function is directly proportional to the normalized function, f ( η ) {\displaystyle f(\eta )} , which is only a function of the

    Blasius boundary layer

    Blasius_boundary_layer

  • Lambert W function
  • Multivalued function in mathematics

    In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse

    Lambert W function

    Lambert W function

    Lambert_W_function

  • Alternating series
  • Infinite series whose terms alternate in sign

    {x}{2}}\right)}^{2m+\alpha }} where Γ(z) is the gamma function. If s is a complex number, the Dirichlet eta function is formed as an alternating series η ( s ) =

    Alternating series

    Alternating_series

  • Held group
  • Sporadic simple group

    }+1956q^{4}+5135q^{5}+\dots \end{aligned}}} and η(τ) is the Dedekind eta function. It can be defined in terms of the generators a and b and relations a

    Held group

    Held group

    Held_group

  • Map (higher-order function)
  • Computer programming function

    transformations correspond to functions of the form eta :: F a -> G a, where a is a universally quantified type variable – eta knows nothing about the type

    Map (higher-order function)

    Map_(higher-order_function)

  • Pentagonal number theorem
  • Theorem in number theory

    Euler's function, which is closely related to the Dedekind eta function, and occurs in the study of modular forms. The modulus of the Euler function (see

    Pentagonal number theorem

    Pentagonal_number_theorem

  • Landau theory
  • Theory of continuous phase transitions

    0=A(T)\eta ^{2}-B_{0}\eta ^{4}+C_{0}\eta ^{6},} 0 = 2 A ( T ) η − 4 B 0 η 3 + 6 C 0 η 5 , {\displaystyle 0=2A(T)\eta -4B_{0}\eta ^{3}+6C_{0}\eta ^{5},}

    Landau theory

    Landau_theory

  • Supersingular prime (algebraic number theory)
  • Prime number with a certain relationship to an elliptic curve

    {\displaystyle \eta (\tau )^{2}\eta (11\tau )^{2}} vanishes modulo p {\displaystyle p} , where η {\displaystyle \eta } is the Dedekind eta function. More generally

    Supersingular prime (algebraic number theory)

    Supersingular_prime_(algebraic_number_theory)

  • Euler summation
  • Summation method for some divergent series

    summation to the zeta function (or rather, to the related Dirichlet eta function) yields (cf. Globally convergent series) 1 1 − 2 k + 1 ∑ i = 0 k 1 2

    Euler summation

    Euler_summation

  • Multiple zeta function
  • Generalizations of the Riemann zeta function

    {H}}_{n}^{(c)}}{(n+1)^{b}}}=\zeta (a,b,{\bar {c}})} As a variant of the Dirichlet eta function we define ϕ ( s ) = 1 − 2 ( s − 1 ) 2 ( s − 1 ) ζ ( s ) {\displaystyle

    Multiple zeta function

    Multiple_zeta_function

  • Heta
  • Archaic letter in the Greek alphabet

    the historical Greek alphabet letter eta (Η) and several of its variants, when used in their original function of denoting the consonant /h/. The letter

    Heta

    Heta

  • List of eponyms of special functions
  • relation Cyclotomic polynomials H. G. Dawson: Dawson function Richard Dedekind: Dedekind eta function Charles F. Dunkl: Dunkl operator, Jacobi–Dunkl operator

    List of eponyms of special functions

    List_of_eponyms_of_special_functions

  • Particular values of the Riemann zeta function
  • Constants of the mathematical zeta function

    In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle

    Particular values of the Riemann zeta function

    Particular values of the Riemann zeta function

    Particular_values_of_the_Riemann_zeta_function

  • Cone-shape distribution function
  • Variation of Cohen's class distribution function

    \left(\eta ,\tau \right)={\frac {\sin \left(\pi \eta \tau \right)}{\pi \eta \tau }}\exp \left(-2\pi \alpha \tau ^{2}\right).} The kernel function in t

    Cone-shape distribution function

    Cone-shape_distribution_function

  • Lerch transcendent
  • Special mathematical function

    {1}{n^{s}}}=\Phi (1,s,1)} The Dirichlet eta function: η ( s ) = ∑ n = 1 ∞ ( − 1 ) n − 1 n s = Φ ( − 1 , s , 1 ) {\displaystyle \eta (s)=\sum _{n=1}^{\infty }{\frac

    Lerch transcendent

    Lerch_transcendent

  • Green's identities
  • Vector calculus formulas relating the bulk with the boundary of a region

    {\boldsymbol {\eta }})={\frac {-1}{4\pi \|\mathbf {x} -{\boldsymbol {\eta }}\|}}~.} Green's third identity states that if ψ is a function that is twice

    Green's identities

    Green's_identities

  • Stochastic gradient descent
  • Optimization algorithm

    sufficiently smooth test function. Then, there exists a constant C > 0 {\textstyle C>0} such that for all η > 0 {\textstyle \eta >0} max k = 0 , … , ⌊ T

    Stochastic gradient descent

    Stochastic_gradient_descent

  • Canonical transformation
  • Coordinate transformation that preserves the form of Hamilton's equations

    (\eta ,t;\alpha )=\eta +\alpha \{\eta ,G(\eta ,t)\}+{\frac {1}{2!}}\alpha ^{2}\{\{\eta ,G(\eta ,t)\},G(\eta ,t)\}+\cdots =e^{-\alpha {\tilde {G}}}\eta }

    Canonical transformation

    Canonical_transformation

  • Conway group Co3
  • Sporadic simple group

    11202q^{3}+49152q^{4}+\dots \end{aligned}}} and η(τ) is the Dedekind eta function. Conway et al. (1985) "ATLAS: Conway group Co3". "ATLAS: Conway group

    Conway group Co3

    Conway group Co3

    Conway_group_Co3

  • Conway group
  • Four finite groups derived from the Leech lattice

    {\eta ^{2}(2\tau )}{\eta (\tau )\,\eta (4\tau )}}\right)^{24}\\&=\left(\left({\frac {\eta (\tau )}{\eta (4\tau )}}\right)^{4}+4^{2}\left({\frac {\eta (4\tau

    Conway group

    Conway group

    Conway_group

  • Classical modular curve
  • Plane algebraic curve

    McKay–Thompson series for the class 2B of the Monster, and η is the Dedekind eta function, then x = ( j 2 + 256 ) 3 j 2 2 , {\displaystyle x={\frac {(j_{2}+256)^{3}}{j_{2}^{2}}}

    Classical modular curve

    Classical_modular_curve

  • Lemniscate constant
  • Ratio of the perimeter of Bernoulli's lemniscate to its diameter

    {\displaystyle \operatorname {\Im } \tau >0} and η {\displaystyle \eta } is the eta function. The above result can be equivalently written as ∑ n = 1 ∞ ν (

    Lemniscate constant

    Lemniscate constant

    Lemniscate_constant

  • Generalized Riemann hypothesis
  • Mathematical conjecture about zeros of L-functions

    L-functions than Dedekind zeta functions lie on critical lines. One example can be Ramanujan L-function related to modular form called Dedekind eta function

    Generalized Riemann hypothesis

    Generalized_Riemann_hypothesis

  • Exceptional object
  • Dedekind eta function and the modular discriminant, which connection is deepened by Monstrous moonshine, a development that related modular functions to the

    Exceptional object

    Exceptional object

    Exceptional_object

  • Two-dimensional critical Ising model
  • Conformal field theory of the 2D Ising model critical point

    q ) {\displaystyle \eta (q)} is the Dedekind eta function, and θ i ( 0 | q ) {\displaystyle \theta _{i}(0|q)} are theta functions of the nome q = e 2

    Two-dimensional critical Ising model

    Two-dimensional_critical_Ising_model

AI & ChatGPT searchs for online references containing ETA FUNCTION

ETA FUNCTION

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ETA FUNCTION

  • ELA
  • Female

    Polish

    ELA

     Pet form of Polish Elżbieta, ELA means "God is my oath." Compare with another form of Ela.

    ELA

  • EFA
  • Female

    Welsh

    EFA

     Welsh form of Greek Eva, EFA means "life." Compare with another form of Efa.

    EFA

  • EMA
  • Female

    Hawaiian

    EMA

     Hawaiian form of Norman French Emma, EMA means "entire, whole." Compare with other forms of Ema.

    EMA

  • ITA
  • Female

    Irish

    ITA

     Variant spelling of Irish Íde, ITA means "industrious." Compare with another form of Ita.

    ITA

  • ZETA
  • Female

    Italian

    ZETA

     Variant spelling of Italian Zita, ZETA means "little girl." Compare with another form of Zeta.

    ZETA

  • EMA
  • Female

    Slovene

    EMA

     Slovene form of English Emily, EMA means "rival." Compare with other forms of Ema.

    EMA

  • EWA
  • Female

    Polish

    EWA

    Hawaiian and Polish form of Greek Eva, EWA means "life."

    EWA

  • ITA
  • Female

    Yiddish

    ITA

    (אִיטָא) Yiddish form of English Yetta, ITA means "little home-ruler." Compare with another form of Ita.

    ITA

  • EMA
  • Female

    Hungarian

    EMA

     Hungarian form of Norman French Emma, EMA means "entire, whole." Compare with other forms of Ema.

    EMA

  • META
  • Female

    German

    META

    Short form of German Margarete, META means "pearl."

    META

  • LETA
  • Female

    Spanish

    LETA

     Short form of Spanish Aleta, LETA means "winged." Compare with another form of Leta.

    LETA

  • ATA
  • Male

    Turkish

    ATA

    Turkish name ATA means "ancestor."

    ATA

  • ETNA
  • Female

    Hebrew

    ETNA

    (אֶתְנָה) Hebrew name ETNA means "hire" or "for hire." Compare with another form of Etna.

    ETNA

  • ELA
  • Female

    Hebrew

    ELA

     Variant spelling of Hebrew Eila, ELA means "oak tree, terebinth tree." Compare with another form of Ela.

    ELA

  • ETTA
  • Female

    English

    ETTA

    Short form of longer Latin names that end with the diminutive suffix -etta, ETTA means "little." 

    ETTA

  • PETA
  • Female

    Native American

    PETA

     Native American Blackfoot name PETA means "golden eagle." Compare with another form of Peta.

    PETA

  • BETA
  • Female

    English

    BETA

    English name derived from the second letter of the Greek alphabet, beta, related to Hebrew bet, BETA means "house." 

    BETA

  • ESTA
  • Female

    English

    ESTA

    English pet form of Persian Esther, ESTA means "star."

    ESTA

  • Cooke
  • Surname or Lastname

    English, etc.

    Cooke

    English, etc. : variant spelling of Cook.

    Cooke

  • ETNA
  • Female

    English

    ETNA

     Variant spelling of English Ethna, ETNA means "kernel." Compare with another form of Etna.

    ETNA

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Online names & meanings

  • Balraj
  • Boy/Male

    Bengali, Celebrity, Gujarati, Hindu, Indian, Malayalam, Marathi, Oriya, Punjabi, Sanskrit, Sikh, Tamil, Telugu, Traditional

    Balraj

    King; Mighty; Powerful; Strong

  • Harshal
  • Girl/Female

    Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi

    Harshal

    Glad; Always Happy

  • Larisa | லாரீஸா 
  • Girl/Female

    Tamil

    Larisa | லாரீஸா 

    Cheerful, Light-hearted

  • Animan
  • Boy/Male

    Hindu

    Animan

    Unbounded

  • Ayeisha
  • Girl/Female

    Arabic

    Ayeisha

    Woman. Life. Aisha was the name of the favorite wife of the prophet Mohammed.

  • Arti
  • Girl/Female

    Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi

    Arti

    Prayer Ceremony; God Worship; Meaningful; Devotion; Hymns Sang in Praise of God

  • Talya
  • Girl/Female

    Hebrew

    Talya

    Dew of heaven.

  • Khatir
  • Boy/Male

    Arabic

    Khatir

    Idea; Heart

  • Hwitcumb
  • Boy/Male

    British, English

    Hwitcumb

    From the White Hollow

  • Worrick
  • Surname or Lastname

    English

    Worrick

    English : variant of Warwick.

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Other words and meanings similar to

ETA FUNCTION

AI search in online dictionary sources & meanings containing ETA FUNCTION

ETA FUNCTION

  • Seta
  • n.

    Any slender, more or less rigid, bristlelike organ or part; as the hairs of a caterpillar, the slender spines of a crustacean, the hairlike processes of a protozoan, the bristles or stiff hairs on the leaves of some plants, or the pedicel of the capsule of a moss.

  • Moth-eat
  • v. t.

    To eat or prey upon, as a moth eats a garment.

  • Tea
  • n.

    The evening meal, at which tea is usually served; supper.

  • Tea
  • n.

    A decoction or infusion of tea leaves in boiling water; as, tea is a common beverage.

  • Tea
  • v. i.

    To take or drink tea.

  • Zeta
  • n.

    A Greek letter corresponding to our z.

  • Eat
  • v. t.

    To chew and swallow as food; to devour; -- said especially of food not liquid; as, to eat bread.

  • Etna
  • n.

    A kind of small, portable, cooking apparatus for which heat is furnished by a spirit lamp.

  • Tea
  • n.

    The prepared leaves of a shrub, or small tree (Thea, / Camellia, Chinensis). The shrub is a native of China, but has been introduced to some extent into some other countries.

  • Tea
  • n.

    Any infusion or decoction, especially when made of the dried leaves of plants; as, sage tea; chamomile tea; catnip tea.

  • Era
  • n.

    A period of time in which a new order of things prevails; a signal stage of history; an epoch.

  • Era
  • n.

    A period of time reckoned from some particular date or epoch; a succession of years dating from some important event; as, the era of Alexander; the era of Christ, or the Christian era (see under Christian).

  • Seta
  • n.

    One of the movable chitinous spines or hooks of an annelid. They usually arise in clusters from muscular capsules, and are used in locomotion and for defense. They are very diverse in form.

  • Seta
  • n.

    One of the spinelike feathers at the base of the bill of certain birds.

  • Eat
  • v. i.

    To make one's way slowly.

  • Era
  • n.

    A fixed point of time, usually an epoch, from which a series of years is reckoned.

  • Eat
  • v. i.

    To taste or relish; as, it eats like tender beef.