• Thumbnail for Inverse gamma function
    In mathematics, the inverse gamma function Γ − 1 ( x ) {\displaystyle \Gamma ^{-1}(x)} is the inverse function of the gamma function. In other words, y...
    6 KB (833 words) - 00:19, 7 May 2025
  • Thumbnail for Inverse-gamma distribution
    distribution differently, as a scaled inverse chi-squared distribution. The inverse gamma distribution's probability density function is defined over the support...
    11 KB (1,632 words) - 09:32, 12 June 2025
  • Thumbnail for Gamma function
    Pseudogamma function Hadamard's gamma function Inverse gamma function Lanczos approximation Multiple gamma function Multivariate gamma function p-adic gamma function...
    90 KB (13,545 words) - 04:27, 29 July 2025
  • Thumbnail for Gamma distribution
    prefer the (α,λ) parameterization, utilizing the gamma distribution as a conjugate prior for several inverse scale parameters, facilitating analytical tractability...
    66 KB (9,095 words) - 06:11, 7 July 2025
  • In mathematics, the inverse Laplace transform of a function F {\displaystyle F} is a real function f {\displaystyle f} that is piecewise-continuous,...
    8 KB (1,032 words) - 12:48, 24 July 2025
  • Thumbnail for Incomplete gamma function
    In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems...
    43 KB (7,178 words) - 19:08, 3 August 2025
  • the only shades that are unaffected by gamma. To compensate for this effect, the inverse transfer function (gamma correction) is sometimes applied to the...
    43 KB (5,360 words) - 19:38, 27 July 2025
  • Thumbnail for Multivalued function
    If f : X → Y is an ordinary function, then its inverse is the multivalued function Γ f − 1   ⊆   Y × X {\displaystyle \Gamma _{f^{-1}}\ \subseteq \ Y\times...
    11 KB (1,432 words) - 11:59, 6 August 2025
  • function, Polygamma function Incomplete beta function Incomplete gamma function K-function Multivariate gamma function: A generalization of the Gamma...
    10 KB (1,065 words) - 21:42, 29 July 2025
  • Thumbnail for Error function
    \end{aligned}}} The inverse of Φ is known as the normal quantile function, or probit function and may be expressed in terms of the inverse error function as probit...
    48 KB (7,358 words) - 08:30, 16 July 2025
  • Thumbnail for Digamma 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 )...
    36 KB (7,152 words) - 22:28, 2 August 2025
  • Thumbnail for Student's t-distribution
    instance of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution...
    55 KB (6,423 words) - 01:28, 22 July 2025
  • Thumbnail for Inverse-chi-squared distribution
    Further, Γ {\displaystyle \Gamma } is the gamma function. The inverse chi-squared distribution is a special case of the inverse-gamma distribution. with shape...
    5 KB (394 words) - 21:42, 12 October 2024
  • Thumbnail for Quantile function
    quantile function is also called the percentile function (after the percentile), percent-point function, inverse cumulative distribution function (after...
    17 KB (2,217 words) - 11:33, 12 July 2025
  • Thumbnail for Reciprocal gamma 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...
    11 KB (1,467 words) - 18:45, 23 June 2025
  • Other inverse distributions include inverse-chi-squared distribution inverse-gamma distribution inverse-Wishart distribution inverse matrix gamma distribution...
    12 KB (1,718 words) - 22:17, 18 March 2025
  • root, and function composition to polynomial, exponential, logarithm, and trigonometric functions. They include inverse trigonometric functions, hyperbolic...
    13 KB (1,520 words) - 09:16, 5 August 2025
  • Thumbnail for Restriction (mathematics)
    restriction of a continuous function is continuous. For a function to have an inverse, it must be one-to-one. If a function f {\displaystyle f} is not...
    11 KB (1,906 words) - 17:20, 28 May 2025
  • /x)}{\Gamma _{1}(\alpha )}}.} i.e., the inverse-gamma distribution, where Γ 1 ( ⋅ ) {\displaystyle \Gamma _{1}(\cdot )} is the ordinary Gamma function. The...
    20 KB (3,491 words) - 15:44, 5 June 2025
  • ( γ ) ( t ) = W ( t ) + γ t {\displaystyle W^{(\gamma )}(t)=W(t)+\gamma t} , we can define the inverse Gaussian process A t = inf { s > 0 : W ( γ ) ( s...
    7 KB (905 words) - 16:16, 10 June 2025
  • Abel discovered elliptic functions by taking the inverse function φ {\displaystyle \varphi } of the elliptic integral function α ( x ) = ∫ 0 x d t ( 1...
    16 KB (2,442 words) - 06:46, 17 July 2025
  • Thumbnail for Normal-inverse-gamma distribution
    In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate...
    12 KB (2,039 words) - 19:52, 19 May 2025
  • Thumbnail for Sine and cosine
    \Gamma } is the gamma function and ϖ {\displaystyle \varpi } is the lemniscate constant. The inverse function of sine is arcsine or inverse sine, denoted...
    56 KB (7,064 words) - 09:28, 28 July 2025
  • Thumbnail for Hypergeometric function
    non-negative integer, one has 2F1(z) → ∞. Dividing by the value Γ(c) of the gamma function, we have the limit: lim c → − m 2 F 1 ( a , b ; c ; z ) Γ ( c ) = (...
    39 KB (6,920 words) - 01:03, 29 July 2025
  • gamma function Γp is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the probability density function of...
    5 KB (958 words) - 12:47, 25 May 2022
  • Thumbnail for Green's function
    Green's function. A Green's function can also be thought of as a right inverse of L. Aside from the difficulties of finding a Green's function for a particular...
    43 KB (5,810 words) - 04:19, 21 July 2025
  • Thumbnail for Clausen function
    polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order...
    31 KB (6,482 words) - 06:52, 8 August 2025
  • Thumbnail for Scaled inverse chi-squared distribution
    alternative parametrization is given by the inverse-gamma distribution. The probability density function of the scaled inverse chi-squared distribution extends over...
    12 KB (2,163 words) - 18:40, 9 March 2025
  • Thumbnail for Sinc function
    their 1952 article "Information theory and inverse probability in telecommunication", saying "This function occurs so often in Fourier analysis and its...
    23 KB (3,296 words) - 04:48, 12 July 2025
  • multiplication can be too, which is doubtful). In fact, both this pairing function and its inverse can be computed with finite-state transducers that run in real...
    15 KB (2,488 words) - 13:28, 9 August 2025