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MULTIPLE GAMMA-FUNCTION

  • Multiple gamma function
  • Generalization of the Euler gamma function and the Barnes G-function

    multiple gamma function Γ N {\displaystyle \Gamma _{N}} is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function

    Multiple gamma function

    Multiple gamma function

    Multiple_gamma_function

  • Gamma function
  • Extension of the factorial function

    the gamma function (represented by ⁠ Γ {\displaystyle \Gamma } ⁠, capital Greek letter gamma) is the most common extension of the factorial function to

    Gamma function

    Gamma function

    Gamma_function

  • Incomplete gamma function
  • Types of special mathematical functions

    In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems

    Incomplete gamma function

    Incomplete gamma function

    Incomplete_gamma_function

  • Particular values of the gamma function
  • Mathematical constants

    The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer, half-integer, and

    Particular values of the gamma function

    Particular_values_of_the_gamma_function

  • Reciprocal gamma function
  • Mathematical function

    reciprocal gamma function is the function f ( z ) = 1 Γ ( z ) , {\displaystyle f(z)={\frac {1}{\Gamma (z)}},} where Γ(z) denotes the gamma function. Since

    Reciprocal gamma function

    Reciprocal gamma function

    Reciprocal_gamma_function

  • Inverse gamma function
  • Inverse of the gamma function

    mathematics, the inverse gamma function Γ − 1 ( x ) {\displaystyle \Gamma ^{-1}(x)} is the inverse function of the gamma function. In other words, y = Γ

    Inverse gamma function

    Inverse gamma function

    Inverse_gamma_function

  • Multivalued function
  • Generalized mathematical function

    In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in

    Multivalued function

    Multivalued function

    Multivalued_function

  • Beta function
  • Mathematical function

    the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial

    Beta function

    Beta function

    Beta_function

  • Q-gamma function
  • Function in q-analog theory

    {\displaystyle q} -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was

    Q-gamma function

    Q-gamma_function

  • Barnes G-function
  • Extension of superfactorials to the complex numbers

    Barnes G-function G ( z ) {\displaystyle G(z)} is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function

    Barnes G-function

    Barnes G-function

    Barnes_G-function

  • Γ₀
  • Topics referred to by the same term

    Γ0 or Gamma 0 may refer to: Feferman–Schütte ordinal Hecke congruence subgroup, Γ0(n) the multiple gamma function, Γn, for n = 0, as used in an inductive

    Γ₀

    Γ₀

  • Gamma distribution
  • Probability distribution

    {\gamma (\alpha ,\beta x)}{\Gamma (\alpha )}},} where γ ( α , β x ) {\displaystyle \gamma (\alpha ,\beta x)} is the lower incomplete gamma function. If

    Gamma distribution

    Gamma distribution

    Gamma_distribution

  • K-function
  • Concept in mathematics

    generalization of the factorial to the gamma function. There are multiple equivalent definitions of the K-function. The direct definition: K ( z ) = ( 2

    K-function

    K-function

  • Barnes zeta function
  • the multiple gamma function", Trans. Camb. Philos. Soc., 19: 374–425 Friedman, Eduardo; Ruijsenaars, Simon (2004), "Shintani–Barnes zeta and gamma functions"

    Barnes zeta function

    Barnes_zeta_function

  • Riemann zeta function
  • Analytic function in mathematics

    {d} x} is the gamma function. The Riemann zeta function is defined for other complex values via analytic continuation of the function defined for σ >

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • Gamma globulin
  • Class of blood proteins

    that gamma globulin causes the spleen to ignore the antibody-tagged platelets, thus allowing them to survive and function. Another theory on how gamma globulin

    Gamma globulin

    Gamma globulin

    Gamma_globulin

  • Cauchy distribution
  • Probability distribution

    distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f ( x ; x 0 , γ ) {\displaystyle f(x;x_{0},\gamma )} is the distribution

    Cauchy distribution

    Cauchy distribution

    Cauchy_distribution

  • Confluent hypergeometric function
  • Solution of a confluent hypergeometric equation

    gamma function Laguerre polynomials Parabolic cylinder function (or Weber function) Poisson–Charlier function Toronto functions Whittaker functions

    Confluent hypergeometric function

    Confluent hypergeometric function

    Confluent_hypergeometric_function

  • Voigt profile
  • Probability distribution

    V(x;\sigma ,\gamma )={\frac {\operatorname {Re} [w(z)]}{{\sqrt {2\pi }}\,\sigma }},} where Re[w(z)] is the real part of the Faddeeva function evaluated for

    Voigt profile

    Voigt profile

    Voigt_profile

  • Prabhakar function
  • {\displaystyle \Gamma (z)} is the well known gamma function defined by Γ ( z ) = ∫ 0 ∞ t z − 1 e − z d z , ℜ ( z ) > 0 {\displaystyle \Gamma (z)=\int _{0}^{\infty

    Prabhakar function

    Prabhakar_function

  • Bohr–Mollerup theorem
  • Theorem in complex analysis

    The theorem characterizes the gamma function, defined for x > 0 by Γ ( x ) = ∫ 0 ∞ t x − 1 e − t d t {\displaystyle \Gamma (x)=\int _{0}^{\infty }t^{x-1}e^{-t}\

    Bohr–Mollerup theorem

    Bohr–Mollerup_theorem

  • Sine and cosine
  • Fundamental trigonometric functions

    the functional equation for the Gamma function, Γ ( s ) Γ ( 1 − s ) = π sin ⁡ ( π s ) , {\displaystyle \Gamma (s)\Gamma (1-s)={\pi \over \sin(\pi s)},}

    Sine and cosine

    Sine and cosine

    Sine_and_cosine

  • Multiplication theorem
  • Identity obeyed by many special functions related to the gamma function

    identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values;

    Multiplication theorem

    Multiplication_theorem

  • Green's function
  • Method of solution to differential equations

    integrals of Green's functions and sums of the same. For example, if L = ( ∂ x + γ ) ( ∂ x + α ) 2 {\displaystyle L=\left(\partial _{x}+\gamma \right)\left(\partial

    Green's function

    Green's function

    Green's_function

  • Stretched exponential function
  • Mathematical function common in physics

    _{K})^{\beta }}={\tau _{K} \over \beta }\Gamma {\left({\frac {1}{\beta }}\right)}} where Γ is the gamma function. For exponential decay, ⟨τ⟩ = τK is recovered

    Stretched exponential function

    Stretched exponential function

    Stretched_exponential_function

  • Pochhammer k-symbol
  • Term in the mathematical theory of special functions

    In the mathematical theory of special functions, the Pochhammer k-symbol and the k-gamma function, introduced by Rafael Díaz and Eddy Pariguan are generalizations

    Pochhammer k-symbol

    Pochhammer_k-symbol

  • Weierstrass–Mandelbrot function
  • Multifractal function used in terrain modeling and simulation

    weierstrass_mandelbrot_3d(x, y, D, G, L, gamma, M, n_max): """ Compute the 3D Weierstrass–Mandelbrot function z(x, y). Parameters: x, y : 2D np.ndarrays

    Weierstrass–Mandelbrot function

    Weierstrass–Mandelbrot function

    Weierstrass–Mandelbrot_function

  • Hankel contour
  • Mathematical concept

    z ) {\displaystyle \Gamma (z+1)=z\Gamma (z)} . The Hankel contour can be used to help derive an expression for the Gamma function, based on the fundamental

    Hankel contour

    Hankel contour

    Hankel_contour

  • Factorial
  • Product of numbers from 1 to n

    factorial function to a continuous function of complex numbers, except at the negative integers, the (offset) gamma function. Many other notable functions and

    Factorial

    Factorial

  • Gradient boosting
  • Machine learning technique

    we can optimize γ {\displaystyle \gamma } by finding the γ {\displaystyle \gamma } value for which the loss function has a minimum: γ m = argmin γ ∑ i

    Gradient boosting

    Gradient_boosting

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

    the function γ ( z ) = ( a z + b ) / ( c z + d ) {\textstyle \gamma (z)=(az+b)/(cz+d)} . The identification of functions with matrices makes function composition

    Modular form

    Modular_form

  • Wishart distribution
  • Generalization of gamma distribution to multiple dimensions

    statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart, who first

    Wishart distribution

    Wishart_distribution

  • Gamma wave
  • Neural oscillation in the 25–140Hz range

    A gamma wave or gamma rhythm is a pattern of neural oscillation in humans with a frequency between 30 and 100 Hz, the 40 Hz point being of particular

    Gamma wave

    Gamma_wave

  • Polylogarithm
  • Special mathematical function

    (Vepstas 2008). Bose integral is result of multiplication between Gamma function and Zeta function. One can begin with equation for Bose integral, then use series

    Polylogarithm

    Polylogarithm

    Polylogarithm

  • Function of several real variables
  • Mathematical function with multiple real-number arguments

    y),\gamma (x,y))=\zeta (\alpha ,\beta ,\gamma )=e^{\alpha }[\sin(3\beta )-\cos(2\gamma )]\,.} Function composition can be used to simplify functions, which

    Function of several real variables

    Function_of_several_real_variables

  • List of trigonometric identities
  • α + β + γ = 180 ∘ , {\displaystyle \alpha +\beta +\gamma =180^{\circ },} as long as the functions occurring in the formulae are well-defined (the latter

    List of trigonometric identities

    List of trigonometric identities

    List_of_trigonometric_identities

  • Liouville field theory
  • Two-dimensional conformal field theory

    iP_{2}\pm iP_{3})}}\ ,} where the special function Υ b {\displaystyle \Upsilon _{b}} is a kind of multiple gamma function. For c ∈ ( − ∞ , 1 ) {\displaystyle

    Liouville field theory

    Liouville_field_theory

  • Ramanujan's master theorem
  • Mathematical theorem

    \int _{0}^{\infty }x^{s-1}f(x)\,dx=\Gamma (s)\,\varphi (-s)} where Γ ( s ) {\textstyle \Gamma (s)} is the gamma function. It was widely used by Ramanujan

    Ramanujan's master theorem

    Ramanujan's master theorem

    Ramanujan's_master_theorem

  • Deflated Sharpe ratio
  • Statistical tool to assess investments

    \Phi ^{-1}} is the quantile function (inverse CDF) of the standard normal distribution, γ ≈ 0.5772 {\displaystyle \gamma \approx 0.5772} is the Euler–Mascheroni

    Deflated Sharpe ratio

    Deflated_Sharpe_ratio

  • Synge's world function
  • Locally defined function in general relativity

    ′ {\displaystyle \gamma (\lambda _{0})=x'} and γ ( λ 1 ) = x {\displaystyle \gamma (\lambda _{1})=x} . Then Synge's world function is defined as: σ (

    Synge's world function

    Synge's_world_function

  • Gamma-ray burst
  • Flash of gamma rays from a distant galaxy

    In gamma-ray astronomy, gamma-ray bursts (GRBs) are extremely energetic events occurring in distant galaxies which represent the brightest and most powerful

    Gamma-ray burst

    Gamma-ray burst

    Gamma-ray_burst

  • Jacobi elliptic functions
  • Mathematical function

    In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as

    Jacobi elliptic functions

    Jacobi_elliptic_functions

  • Leverett J-function
  • Function in fluid dynamics

    The J-function is defined as: J ( S w ) = p c ( S w ) k / ϕ γ cos ⁡ θ {\displaystyle J(S_{w})={\frac {p_{c}(S_{w}){\sqrt {k/\phi }}}{\gamma \cos \theta

    Leverett J-function

    Leverett_J-function

  • Modified half-normal distribution
  • Probability distribution

    generalization of multiple families, including the half-normal distribution, truncated normal distribution, gamma distribution, and square root of the gamma distribution

    Modified half-normal distribution

    Modified_half-normal_distribution

  • Nyquist stability criterion
  • Graphical method of determining the stability of a dynamical system

    {\displaystyle \Gamma _{s}} drawn in the complex s {\displaystyle s} plane, encompassing but not passing through any number of zeros and poles of a function F ( s

    Nyquist stability criterion

    Nyquist stability criterion

    Nyquist_stability_criterion

  • Γ-Hydroxybutyric acid
  • Chemical compound

    γ-Hydroxybutyric acid, also known as gamma-hydroxybutyric acid, GHB, or 4-hydroxybutanoic acid, is a naturally occurring neurotransmitter and a depressant

    Γ-Hydroxybutyric acid

    Γ-Hydroxybutyric acid

    Γ-Hydroxybutyric_acid

  • Euler's totient function
  • Number of integers coprime to and less than n

    {\displaystyle \gamma } is Euler's constant and p 120569 # {\displaystyle p_{120569}\#} is the product of the first 120569 primes. Carmichael function (λ) Dedekind

    Euler's totient function

    Euler's totient function

    Euler's_totient_function

  • Cobb–Douglas production function
  • Economic formula of productivity

    production function (in the two-factor case) is Y = A ( α L γ + ( 1 − α ) K γ ) 1 / γ , {\displaystyle Y=A\left(\alpha L^{\gamma }+(1-\alpha )K^{\gamma }\right)^{1/\gamma

    Cobb–Douglas production function

    Cobb–Douglas production function

    Cobb–Douglas_production_function

  • Morera's theorem
  • Integral criterion for holomorphy

    _{n=1}^{\infty }{\frac {1}{n^{s}}}} or the Gamma function Γ ( α ) = ∫ 0 ∞ x α − 1 e − x d x . {\displaystyle \Gamma (\alpha )=\int _{0}^{\infty }x^{\alpha

    Morera's theorem

    Morera's theorem

    Morera's_theorem

  • Decentralized partially observable Markov decision process
  • Model for coordination and decision-making among multiple agents

    , { Ω i } , O , γ ) {\displaystyle (S,\{A_{i}\},T,R,\{\Omega _{i}\},O,\gamma )} , where S {\displaystyle S} is a set of states, A i {\displaystyle A_{i}}

    Decentralized partially observable Markov decision process

    Decentralized_partially_observable_Markov_decision_process

  • Student's t-distribution
  • Probability distribution

    is the number of degrees of freedom, and Γ {\displaystyle \Gamma } is the gamma function. This may also be written as f ( t ) = 1 ν B ( 1 2 , ν 2 ) (

    Student's t-distribution

    Student's t-distribution

    Student's_t-distribution

  • Double factorial
  • Mathematical function

    everywhere it is defined. As with the gamma function that extends the ordinary factorial function, this double factorial function is logarithmically convex in

    Double factorial

    Double factorial

    Double_factorial

  • Meijer G-function
  • Generalization of the hypergeometric function

    (1-b_{j}+s)\prod _{j=n+1}^{p}\Gamma (a_{j}-s)}}\,z^{s}\,ds,} where Γ denotes the gamma function. This integral is of the so-called Mellin–Barnes type, and may be viewed

    Meijer G-function

    Meijer G-function

    Meijer_G-function

  • Dirichlet distribution
  • Probability distribution

    normalizing constant is the multivariate beta function, which can be expressed in terms of the gamma function: B ( α ) = ∏ i = 1 K Γ ( α i ) Γ ( ∑ i = 1

    Dirichlet distribution

    Dirichlet distribution

    Dirichlet_distribution

  • Negative binomial distribution
  • Probability distribution

    {(k+r-1)(k+r-2)\dotsm (r)}{k!}}={\frac {\Gamma (k+r)}{k!\ \Gamma (r)}}=\left(\!\!{r \choose k}\!\!\right).} Note that Γ(r) is the Gamma function, and ( ( r k ) ) {\displaystyle

    Negative binomial distribution

    Negative binomial distribution

    Negative_binomial_distribution

  • Hinge loss
  • Loss function in machine learning

    loss L {\displaystyle L} is a special case of this loss function with γ = 2 {\displaystyle \gamma =2} , specifically L ( t , y ) = 4 ℓ 2 ( y ) {\displaystyle

    Hinge loss

    Hinge loss

    Hinge_loss

  • Hamilton–Jacobi equation
  • Formulation of classical mechanics

    {\displaystyle \gamma =\gamma (\tau ;t,t_{0},\mathbf {q} ,\mathbf {q} _{0})} be the (unique) extremal from the definition of the Hamilton's principal function ⁠ S

    Hamilton–Jacobi equation

    Hamilton–Jacobi_equation

  • Volume of an n-ball
  • Size of a mathematical ball

    recurrence relation. Closed-form expressions involve the gamma, factorial, or double factorial function. The volume can also be expressed in terms of A n {\displaystyle

    Volume of an n-ball

    Volume of an n-ball

    Volume_of_an_n-ball

  • Dirichlet eta function
  • Function in analytic number theory

    positive real part ( Γ ( s ) {\displaystyle \Gamma (s)} represents the gamma function). This gives the eta function as a Mellin transform. Hardy gave a simple

    Dirichlet eta function

    Dirichlet eta function

    Dirichlet_eta_function

  • Ordinal notation
  • Type of mathematical function

    {\displaystyle \gamma } such that α < γ {\displaystyle \alpha <\gamma } and β < γ {\displaystyle \beta <\gamma } and γ {\displaystyle \gamma } is not the

    Ordinal notation

    Ordinal_notation

  • Erlang distribution
  • Family of continuous probability distributions

    {\gamma (k,\lambda x)}{\Gamma (k)}}={\frac {\gamma (k,\lambda x)}{(k-1)!}},} where γ {\displaystyle \gamma } is the lower incomplete gamma function and

    Erlang distribution

    Erlang distribution

    Erlang_distribution

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

    first need to expand the part of the log-partition function that involves the multivariate gamma function: log ⁡ Γ p ( a ) = log ⁡ ( π p ( p − 1 ) 4 ∏ j =

    Exponential family

    Exponential_family

  • Paschen's law
  • Physical law about electrical discharge in gases

    possible multiple ionizations of the same atom, the number of created ions is the same as the number of created electrons: Γ i {\displaystyle \Gamma _{i}}

    Paschen's law

    Paschen's law

    Paschen's_law

  • Temporal difference learning
  • Computer programming concept

    {\displaystyle V^{\pi }(s)=E_{\pi }\{R_{1}+\gamma V^{\pi }(S_{1})|S_{0}=s\},} so R 1 + γ V π ( S 1 ) {\displaystyle R_{1}+\gamma V^{\pi }(S_{1})} is an unbiased estimate

    Temporal difference learning

    Temporal_difference_learning

  • Policy gradient method
  • Class of reinforcement learning algorithms

    S_{t})\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau }){\Big |}S_{0}=s_{0}\right]} Lemma—The expectation of the score function is zero, conditional on any

    Policy gradient method

    Policy_gradient_method

  • Kriging
  • Method of interpolation

    ( h ) . {\displaystyle \gamma {\big (}Z(x_{1}),Z(x_{2}){\big )}=\gamma {\big (}Z(x_{i}),Z(x_{i}+\mathbf {h} ){\big )}=\gamma (h).} For simplicity, we

    Kriging

    Kriging

    Kriging

  • Augmented Dickey–Fuller test
  • Time series statistical test

    function ndiffs handles multiple popular unit root tests package tseries function adf.test package fUnitRoots function adfTest package urca function ur

    Augmented Dickey–Fuller test

    Augmented_Dickey–Fuller_test

  • Indefinite sum
  • Inverse of a finite difference

    the Gamma function: ∑ x Γ ( x + 1 ) Γ ( x − n + 1 ) = Γ ( x + 1 ) ( n + 1 ) Γ ( x − n ) + C ( x ) , n ≠ − 1. {\displaystyle \sum _{x}{\frac {\Gamma

    Indefinite sum

    Indefinite sum

    Indefinite_sum

  • Differentiation rules
  • Rules for computing derivatives of functions

    {1}{x+n}}\right)-{\dfrac {1}{x}}\right)\\&=\Gamma (x)\psi (x),\end{aligned}}} with ψ ( x ) {\textstyle \psi (x)} being the digamma function, expressed by the parenthesized

    Differentiation rules

    Differentiation_rules

  • Contour integration
  • Method of evaluating certain integrals along paths in the complex plane

    f(t)={\frac {1}{2\pi i}}\int _{\gamma -i\infty }^{\gamma +i\infty }e^{st}F(s)\,ds} This integral expresses a function f ( t ) {\displaystyle f(t)} in

    Contour integration

    Contour_integration

  • Nakagami distribution
  • Statistical distribution

    }}x^{2}\right)}{\Gamma (m)}}=P\left(m,{\frac {m}{\Omega }}x^{2}\right)} where P is the regularized (lower) incomplete gamma function. The parameters m

    Nakagami distribution

    Nakagami distribution

    Nakagami_distribution

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    (n)}}<e^{\gamma }\log \log n+{\frac {e^{\gamma }(4+\gamma -\log 4\pi )}{\sqrt {\log n}}}} is true for all n ≥ 120569#, where φ(n) is Euler's totient function and

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • Gamma-glutamyl carboxylase
  • Enzyme

    Gamma-glutamyl carboxylase is an enzyme that in humans is encoded by the GGCX gene, located on chromosome 2 at 2p12. Gamma-glutamyl carboxylase is an enzyme

    Gamma-glutamyl carboxylase

    Gamma-glutamyl carboxylase

    Gamma-glutamyl_carboxylase

  • Entire function
  • Function that is holomorphic on the whole complex plane

    sigma function. Other examples include the Fresnel integrals, the Jacobi theta function, and the reciprocal Gamma function. The exponential function and

    Entire function

    Entire_function

  • Dynamic light scattering
  • Technique for determining size distribution of particles

    g^{1}(q;\tau )=\sum _{i=1}^{n}G_{i}(\Gamma _{i})\exp(-\Gamma _{i}\tau )=\int G(\Gamma )\exp(-\Gamma \tau )\,d\Gamma .} It is tempting to obtain data for

    Dynamic light scattering

    Dynamic light scattering

    Dynamic_light_scattering

  • Lévy distribution
  • Probability distribution

    It is a special case of the inverse-gamma distribution and a stable distribution. The probability density function of the Lévy distribution over the domain

    Lévy distribution

    Lévy distribution

    Lévy_distribution

  • General Coordinates Network
  • System distributing location information about gamma-ray bursts

    instrument on the Compton Gamma-Ray Observatory (CGRO), and BACODINE monitored the BATSE real-time telemetry from CGRO. The first function of BACODINE was calculating

    General Coordinates Network

    General Coordinates Network

    General_Coordinates_Network

  • Beta distribution
  • Probability distribution

    -1}\end{aligned}}} where Γ ( z ) {\displaystyle \Gamma (z)} is the gamma function. The beta function, B {\displaystyle \mathrm {B} } , is a normalization

    Beta distribution

    Beta distribution

    Beta_distribution

  • Laguerre polynomials
  • Sequence of differential equation solutions

    }}\Re (\gamma )>-{\tfrac {1}{2}}} for the exponential function. The incomplete gamma function has the representation Γ ( α , x ) = x α e − x ∑ i = 0

    Laguerre polynomials

    Laguerre polynomials

    Laguerre_polynomials

  • Walsh function
  • Concept in mathematics

    Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be

    Walsh function

    Walsh_function

  • Window function
  • Function used in signal processing

    processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside

    Window function

    Window function

    Window_function

  • Meir–Wingreen formula
  • Equation in quantum transport

    \mathrm {Tr} \left[(\Gamma ^{\mathrm {L} }-\Gamma ^{\mathrm {R} })G^{\mathrm {K} }-(\Gamma ^{\mathrm {L} }f_{\mathrm {L} }-\Gamma ^{\mathrm {R} }f_{\mathrm

    Meir–Wingreen formula

    Meir–Wingreen_formula

  • Binomial coefficient
  • Number of subsets of a given size

    generalized to two real or complex valued arguments using the gamma function or beta function via ( x y ) = Γ ( x + 1 ) Γ ( y + 1 ) Γ ( x − y + 1 ) = 1 (

    Binomial coefficient

    Binomial coefficient

    Binomial_coefficient

  • Duncan's new multiple range test
  • Multiple comparison procedure

    α p = 1 − γ p {\displaystyle \alpha _{p}=1-\gamma _{p}} , γ p = ( 1 − α ) ( p − 1 ) {\displaystyle \gamma _{p}=(1-\alpha )^{(p-1)}} and p {\displaystyle

    Duncan's new multiple range test

    Duncan's_new_multiple_range_test

  • Integration by parts
  • Mathematical method in calculus

    \end{aligned}}} may be derived using integration by parts. The gamma function is an example of a special function, defined as an improper integral for z > 0 {\displaystyle

    Integration by parts

    Integration_by_parts

  • Studentized range distribution
  • f_{\text{R}}(q;k,\nu )={\frac {{\sqrt {2\pi \,}}\,k\,(k-1)\,\nu ^{\nu /2}}{\Gamma (\nu /2)\,2^{\left(\nu /2-1\right)}}}\int _{0}^{\infty }s^{\nu }\,\varphi

    Studentized range distribution

    Studentized range distribution

    Studentized_range_distribution

  • Pluripotency (biological compounds)
  • Ability of certain substances to produce several distinct biological responses

    so they can be attacked, among other functions. TH1 cells are created to make cytokines, like interferon gamma, that activate macrophages and cytotoxic

    Pluripotency (biological compounds)

    Pluripotency_(biological_compounds)

  • Analytic combinatorics
  • Field of combinatorics using complex analysis

    {n^{-\alpha -1}}{\Gamma (-\alpha )}}(\log n)^{\gamma }(\log \log n)^{\delta }\quad } as n → ∞ {\displaystyle n\to \infty } For generating functions including

    Analytic combinatorics

    Analytic_combinatorics

  • Multiple myeloma
  • Cancer of plasma cells

    kidney function may develop, either acutely or chronically, and with any degree of severity. The most common cause of kidney failure in multiple myeloma

    Multiple myeloma

    Multiple myeloma

    Multiple_myeloma

  • Single-photon emission computed tomography
  • Nuclear medicine tomographic imaging technique

    the function of interest. SPECT imaging is performed by using a gamma camera to acquire multiple 2-D images (also called projections), from multiple angles

    Single-photon emission computed tomography

    Single-photon emission computed tomography

    Single-photon_emission_computed_tomography

  • Sinc function
  • Special mathematical function defined as sin(x)/x

    }\left(1-{\frac {x^{2}}{n^{2}}}\right)} and is related to the gamma function Γ(x), as well as to Gauss' Pi function, through Euler's reflection formula: sin ⁡ ( π x

    Sinc function

    Sinc function

    Sinc_function

  • Markov decision process
  • Mathematical model for sequential decision making under uncertainty

    V^{*}(s)=\max _{a}E\left[R_{a}(s,s')+\gamma V^{*}(s')\right]} From inspection, notice that this fixed point is the value function associated to the following policy

    Markov decision process

    Markov_decision_process

  • Falling and rising factorials
  • Mathematical functions

    coefficients, or any complex-valued function. Falling factorials appear in multiple differentiation of simple power functions: ( d d x ) n x a = ( a ) n ⋅ x

    Falling and rising factorials

    Falling_and_rising_factorials

  • Lambert W function
  • Multivalued function in mathematics

    {1}{N}}}\Gamma \left(1-{\frac {1}{N}}\right)\qquad {\text{for }}N>1\end{aligned}}} where Γ {\displaystyle \Gamma } denotes the gamma function. The first

    Lambert W function

    Lambert W function

    Lambert_W_function

  • Fractional calculus
  • Branch of mathematical analysis

    a generalization for real n: using the gamma function to remove the discrete nature of the factorial function gives us a natural candidate for applications

    Fractional calculus

    Fractional_calculus

  • Regularization (mathematics)
  • Technique to make a model more generalizable and transferable

    {\gamma }{n}}{\hat {X}}^{\mathsf {T}}{\hat {X}}\right){\frac {\gamma }{n}}\sum _{i=0}^{T-2}\left(I-{\frac {\gamma }{n}}{\hat {X}}^{\mathsf

    Regularization (mathematics)

    Regularization (mathematics)

    Regularization_(mathematics)

  • Gammatone filter
  • Linear filter

    sinusoid (a pure tone) with an amplitude envelope which is a scaled gamma distribution function. Gammatone filterbank cepstral coefficients (GFCCs) are auditory

    Gammatone filter

    Gammatone filter

    Gammatone_filter

  • Distribution of the product of two random variables
  • Probability distribution

    } where W is the Whittaker function while β = n 1 − ρ , γ = n 1 + ρ {\displaystyle \beta ={\frac {n}{1-\rho }},\;\;\gamma ={\frac {n}{1+\rho }}} . Using

    Distribution of the product of two random variables

    Distribution_of_the_product_of_two_random_variables

  • GNU MPFR
  • C library for arbitrary-precision floating-point arithmetic

    exp(x)−1 functions (log1p and expm1), the six trigonometric and hyperbolic functions and their inverses, the gamma, zeta and error functions, the arithmetic–geometric

    GNU MPFR

    GNU MPFR

    GNU_MPFR

  • Hessian matrix
  • Matrix of second derivatives

    partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix

    Hessian matrix

    Hessian_matrix

AI & ChatGPT searchs for online references containing MULTIPLE GAMMA-FUNCTION

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  • Gamya
  • Girl/Female

    Hindu, Indian, Kannada, Telugu

    Gamya

    Beautiful; A Destiny

    Gamya

  • Anwaar
  • Boy/Male

    Muslim

    Anwaar

    Multiple lights. Luster.

    Anwaar

  • Vridhesh
  • Boy/Male

    Hindu, Indian, Tamil

    Vridhesh

    Multiple

    Vridhesh

  • Jooseppi
  • Boy/Male

    Hebrew

    Jooseppi

    God will multiply.

    Jooseppi

  • Josephus
  • Boy/Male

    Hebrew American Latin

    Josephus

    God will multiply.

    Josephus

  • Amma
  • Girl/Female

    Norse

    Amma

    Grandmother.

    Amma

  • Tamma
  • Girl/Female

    Hebrew

    Tamma

    Without flaw.

    Tamma

  • Damma
  • Girl/Female

    Gujarati, Hindu, Indian

    Damma

    The Soothing Voice

    Damma

  • Kamma
  • Girl/Female

    Danish, Indian, Latin, Sanskrit, Swedish

    Kamma

    Loveable; Desire

    Kamma

  • Thai
  • Boy/Male

    Australian, Vietnamese

    Thai

    Many; Multiple

    Thai

  • Tamma
  • Girl/Female

    Australian, French, Hebrew

    Tamma

    Without Flaw; Palm Tree; Perfect

    Tamma

  • Joseba
  • Boy/Male

    Hebrew

    Joseba

    God will multiply.

    Joseba

  • Samma
  • Girl/Female

    Arabic, Indian, Kashmiri

    Samma

    Beautiful Sky

    Samma

  • Agnit
  • Boy/Male

    Hindu, Indian

    Agnit

    Un Countable; Multiple; Countless

    Agnit

  • Amma
  • Boy/Male

    African, British, English, Indian

    Amma

    Mother; God-like

    Amma

  • Amma
  • Boy/Male

    Indian

    Amma

    Supreme god.

    Amma

  • GEMMA
  • Female

    English

    GEMMA

    Italian name GEMMA means "precious stone."

    GEMMA

  • Yusef
  • Boy/Male

    Hebrew

    Yusef

    God shall multiply.

    Yusef

  • Gemma
  • Girl/Female

    French Latin Italian

    Gemma

    Jewel.

    Gemma

  • Gemma
  • Girl/Female

    African, American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Irish, Italian, Jamaican, Latin

    Gemma

    Jewel; Precious Stone; Gem

    Gemma

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Online names & meanings

  • Aebba
  • Girl/Female

    British, English

    Aebba

    Pure

  • Neelimaa | நீலிமா
  • Girl/Female

    Tamil

    Neelimaa | நீலிமா

    Blue complexioned

  • Muhammad
  • Boy/Male

    Muslim/Islamic

    Muhammad

    Praiseworthy - name of the LAST Prophet (A.S)

  • Saqlain
  • Boy/Male

    Indian

    Saqlain

    Two worlds, World and hereafter

  • Brotherton
  • Surname or Lastname

    English

    Brotherton

    English : habitational name from either of two places called Brotherton, in North Yorkshire and Suffolk; both are named with Old English brōðor ‘brother’ or the Old Scandinavian personal name Bróðir + Old English tūn ‘farmstead’, ‘enclosure’.

  • Deepaprabha
  • Girl/Female

    Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi

    Deepaprabha

    Fully Lighted

  • Lece
  • Girl/Female

    British, English

    Lece

    Happy

  • Sameenah
  • Girl/Female

    Indian

    Sameenah

    Valuable, Costly, Precious

  • Sajinder
  • Boy/Male

    Sikh

    Sajinder

    One in equipoise and tranquillity

  • Yasheena | یاشینا
  • Girl/Female

    Muslim

    Yasheena | یاشینا

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MULTIPLE GAMMA-FUNCTION

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  • Mam
  • n.

    Mamma.

  • Multiple
  • n.

    A quantity containing another quantity a number of times without a remainder.

  • Gamba
  • n.

    A viola da gamba.

  • Multiplicator
  • n.

    The number by which another number is multiplied; a multiplier.

  • Mammae
  • pl.

    of Mamma

  • Multiplicative
  • a.

    Tending to multiply; having the power to multiply, or incease numbers.

  • Multiplying
  • p. pr. & vb. n.

    of Multiply

  • Multiplicand
  • n.

    The number which is to be multiplied by another number called the multiplier. See Note under Multiplication.

  • Multiplier
  • n.

    One who, or that which, multiplies or increases number.

  • Gummata
  • pl.

    of Gumma

  • Multiply
  • v. t.

    To add (any given number or quantity) to itself a certain number of times; to find the product of by multiplication; thus 7 multiplied by 8 produces the number 56; to multiply two numbers. See the Note under Multiplication.

  • Propagate
  • v. t.

    To multiply; to increase.

  • Multiplied
  • imp. & p. p.

    of Multiply

  • Multiflue
  • a.

    Having many flues; as, a multiflue boiler. See Boiler.

  • Multiple
  • a.

    Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts.

  • Gamma
  • n.

    The third letter (/, / = Eng. G) of the Greek alphabet.

  • Multiplier
  • n.

    The number by which another number is multiplied. See the Note under Multiplication.

  • Gemmae
  • pl.

    of Gemma

  • Multiplex
  • a.

    Manifold; multiple.

  • Mama
  • n.

    See Mamma.