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Topics referred to by the same term
J-function may refer to: The Klein j-invariant or j function in mathematics Leverett J-function in petroleum engineering This disambiguation page lists
J-function
Modular function in mathematics
In mathematics, the j-invariant or j function is a modular function of weight zero for the special linear group SL ( 2 , Z ) {\displaystyle \operatorname
J-invariant
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Family of solutions to related differential equations
gamma function has simple poles at each of the non-positive integers): J − n ( x ) = ( − 1 ) n J n ( x ) . {\displaystyle J_{-n}(x)=(-1)^{n}J_{n}(x)
Bessel_function
Function in fluid dynamics
In fluid dynamics and geology, the Leverett J-function is a dimensionless function used to describe the capillary pressure required to force a fluid into
Leverett_J-function
Extension of the factorial function
gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter gamma), is the most common extension of the factorial function to complex
Gamma_function
Analytic function in mathematics
Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ {\displaystyle \zeta } (zeta), is a function of a complex
Riemann_zeta_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Function specifying the behavior of a component in an electronic or control system
a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models
Transfer_function
In mathematics, the Weber modular functions are a family of three functions f, f1, and f2, studied by Heinrich Martin Weber. Let q = e 2 π i τ {\displaystyle
Weber_modular_function
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Multivalued function in mathematics
j + 1 = w j − w j e w j − z w j e w j + e w j − ( w j + 2 ) ( w j e w j − z ) 2 w j + 2 {\displaystyle w_{j+1}=w_{j}-{\frac {w_{j}e^{w_{j}}-z}{w_{j
Lambert_W_function
S-shaped curve
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac
Logistic_function
Smooth approximation of one-hot arg max
softmax function σ:ℝK→(0,1)K, where K>1, takes a tuple 𝐳=(z1,…,zK)∈ℝK and computes each component of vector σ(𝐳)∈(0,1)K with σ(𝐳)i=ezi∑j=1Kezj. In
Softmax_function
Formal power series
generating function ∑ n = 0 ∞ n ! ( n − j ) ! z n = j ! ⋅ z j ( 1 − z ) j + 1 , {\displaystyle \sum _{n=0}^{\infty }{\frac {n!}{(n-j)!}}\,z^{n}={\frac {j!\cdot
Generating_function
Continued fraction closely related to the Rogers–Ramanujan identities
}} denotes the infinite q-Pochhammer symbol, j is the j-function, and 2F1 is the hypergeometric function. The Rogers–Ramanujan continued fraction is then
Rogers–Ramanujan continued fraction
Rogers–Ramanujan_continued_fraction
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the
Likelihood_function
Monster and modular connection
unexpected connection between the monster group M and modular functions, in particular the j function. The initial numerical observation was made by John McKay
Monstrous_moonshine
function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that
Nearest neighbour distribution
Nearest_neighbour_distribution
Fast-growing function
Friedman's SSCG function is a mathematical function defined by Harvey Friedman. It is defined by SSCG ( k ) {\displaystyle {\text{SSCG}}(k)} as the largest
Friedman's_SSCG_function
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Linear combination of indicator functions of real intervals
mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals
Step_function
Theorem in mathematics
mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that if
Inverse_function_theorem
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Programming language
FL, J supports function-level programming via its tacit programming features. Unlike most languages that support object-oriented programming, J's flexible
J_(programming_language)
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Artificial neural network node function
In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and
Activation_function
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Mathematical function, used to describe magnetization
Langevin function could then be seen as a special case of the more general Brillouin function if the quantum number J {\displaystyle J} was infinite ( J → ∞
Brillouin and Langevin functions
Brillouin_and_Langevin_functions
Anger function, introduced by C. T. Anger (1855), is a function defined as J ν ( z ) = 1 π ∫ 0 π cos ( ν θ − z sin θ ) d θ {\displaystyle \mathbf {J} _{\nu
Anger_function
Mathematical equation
} At least four methods to find the j-function inverse can be given. Dedekind defines the j-function by its Schwarz derivative in his letter to
Picard–Fuchs_equation
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
2-dimensional polar coordinate function
This function is frequently used in image processing.[failed verification] It can be defined through the Bessel function of the first kind ( J 1 {\displaystyle
Sombrero_function
Generalization of the Meijer G-function and the Fox–Wright function
1 2 π i ∫ L ∏ j = 1 m Γ ( b j + B j s ) ∏ j = 1 n Γ ( 1 − a j − A j s ) ∏ j = m + 1 q Γ ( 1 − b j − B j s ) ∏ j = n + 1 p Γ ( a j + A j s ) z − s d s
Fox_H-function
Indicator function of rational numbers
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle
Dirichlet_function
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass function (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_function)
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted
Exponential_function
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_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
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f\colon U\to \mathbb
Harmonic_function
Mathematical function
y = ∑ j = j 0 ∞ a j t j = ∑ j = j 0 ∞ a j ( x − x 0 ) j / e . {\displaystyle y=\sum _{j=j_{0}}^{\infty }a_{j}t^{j}=\sum _{j=j_{0}}^{\infty }a_{j}(x-x_{0})^{j/e}
Algebraic_function
Algebraic variety
zero means such a function field has a single transcendental function as generator: for example the j-function generates the function field of X(1) = PSL(2
Modular_curve
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Types of special mathematical functions
defined similarly to the gamma function but with different or "incomplete" integral limits. The usual gamma function is defined as an integral from zero
Incomplete_gamma_function
Tent function, often used in signal processing
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often
Triangular_function
Generalization of the Jack polynomial
polynomials and Macdonald polynomials. The Jack function J κ ( α ) ( x 1 , x 2 , … , x m ) {\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m})}
Jack_function
Multiplicative function in number theory
(n),} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta, λ ( n ) {\displaystyle \lambda (n)} is the Liouville function, and ω ( n ) {\displaystyle
Möbius_function
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/), denoted by sinc(x), is defined as either sinc ( x ) = sin x x {\displaystyle
Sinc_function
Ratio of polynomial functions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator
Rational_function
Evaluation of a function on its argument
f(g(h(j(x)))) can be rewritten as: f$g$h$j$x This can be equivalently expressed using function composition as: (f∘g∘h∘j)(x) or even: (f∘g∘h∘j∘x)() if
Function_application
Real function with secant line between points above the graph itself
function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function
Convex_function
spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined in relation
Spherical contact distribution function
Spherical_contact_distribution_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
Type of energy
In solid-state physics, the work function is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the
Work_function
Function used as a performance test problem for optimization algorithms
In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance
Rosenbrock_function
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Element of a basis for a function space
functions are ℓ i ( x ) = ∏ j = 0 , j ≠ i n x − x j x i − x j , {\displaystyle \ell _{i}(x)=\prod _{j=0,\ j\neq i}^{n}{\frac {x-x_{j}}{x_{i}-x_{j}}}
Basis_function
Function representing the number of primes less than or equal to a given number
which are divisible by no pi is ⌊x⌋−∑i⌊xpi⌋+∑i<j⌊xpipj⌋−∑i<j<k⌊xpipjpk⌋+⋯ (where ⌊x⌋ denotes the floor function). This number is therefore equal to π(x)−π(x)+1
Prime-counting_function
Function defined by multiple sub-functions
mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned
Piecewise_function
Function uniquely mapping two numbers into a single number
pairing function: ⟨ i , j ⟩ := 1 2 ( i + j − 2 ) ( i + j − 1 ) + i {\displaystyle \langle i,j\rangle :={\frac {1}{2}}(i+j-2)(i+j-1)+i} , where i , j ∈ { 1
Pairing_function
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
is a function of two variables, usually non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j = { 0 if i ≠ j , 1
Kronecker_delta
Mathematical approximation of a function
of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the
Taylor_series
Meromorphic function on the complex plane
An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory
L-function
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Operation on mathematical functions
two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function f ∘ g {\displaystyle f\circ g} . When the composite function f ∘
Function_composition
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
Mathematical function such that every output has at least one input
surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there
Surjective_function
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
Smooth and compactly supported function
analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used
Bump_function
Function that returns its argument unchanged
mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value
Identity_function
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
Mathematical function
allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the
Generalised_logistic_function
Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of
Wave_function_collapse
Cryptographic hash function
BLAKE is a cryptographic hash function based on Daniel J. Bernstein's ChaCha stream cipher, but a permuted copy of the input block, XORed with round constants
BLAKE_(hash_function)
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
Function with a multiplicative scaling behaviour
mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by
Homogeneous_function
Arithmetical function
Jordan's totient function, denoted as J k ( n ) {\displaystyle J_{k}(n)} , where k {\displaystyle k} is a positive integer, is a function of a positive integer
Jordan's_totient_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Statistical function that defines the quantiles of a probability distribution
the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the quantile function of a distribution
Quantile_function
Model of electrical resistance
or tunnel) from one site to another. In the t-J model, instead of U, there is the parameter J, function of the ratio t/U. Like the Hubbard model, it is
T-J_model
Sexual health concept
Sexual function is how the body reacts in different stages of the sexual response cycle. It is defined as the ability of an individual to react sexually
Sexual_function
Number of integers coprime to and less than n
often called Euler's phi function or simply the phi function. In 1879, J. J. Sylvester coined the term totient for this function, so it is also referred
Euler's_totient_function
Cryptographic hash function
The j {\displaystyle j} -th step function Step j {\displaystyle {\textrm {Step}}_{j}} having two inputs T {\displaystyle {\textsf {T}}} and M j ( i )
LSH_(hash_function)
Class of mathematical functions
In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences
Supermodular_function
Mathematical function on a space that is invariant under the action of some group
{\displaystyle f} is the function j {\displaystyle j} . An automorphic function is an automorphic form for which j {\displaystyle j} is the identity. Some
Automorphic_function
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Mathematical conjecture
In the modular setting the transcendental function under consideration is the j {\displaystyle j} -function. Its algebraic properties are governed by
Existential closedness conjecture
Existential_closedness_conjecture
Concept in mathematics
formula for the gamma function: ∏ j = 1 n − 1 Γ ( j n ) = ( 2 π ) n − 1 n {\displaystyle \prod _{j=1}^{n-1}\Gamma \left({\frac {j}{n}}\right)={\sqrt {\frac
K-function
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
Mathematical functions related to Weierstrass's elliptic function
} and a j {\displaystyle a_{j}} are the zeros in the parallelogram and b j {\displaystyle b_{j}} are the poles The Weierstrass zeta function is defined
Weierstrass sigma, zeta, and eta functions
Weierstrass_sigma,_zeta,_and_eta_functions
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Function that is holomorphic on the whole complex plane
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane
Entire_function
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J FUNCTION
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J FUNCTION
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