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...'s gamma function plotted over part of the real axis. Unlike the classical gamma function, it is holomorphic; there are no poles.]] ...real number|real]] and [[complex number]]s in a different way than Euler's gamma function. It is defined as: ...

...idem Aşçıoğlu |date=September 2015 |title=The Generalized Incomplete Gamma Functions |publisher=Eastern Mediterranean University |s2cid=126117454 |url=https://p :<math>\gamma(\alpha,x;b)=\int_0^xt^{\alpha-1}e^{-t-\frac{b}{t}}~dt</math> ...

...nequality''' is an [[inequality (mathematics)|inequality]] for ratios of [[gamma function]]s. It is named after [[Walter Gautschi]]. ...et <math>s\in (0,1)</math>. Then,<ref>NIST Digital Library of Mathematical Functions, 5.6.4.</ref> ...

...1989422}}</ref> The two most famous pseudogamma functions are [[Hadamard's gamma function]], ...- \frac{x}{2}\right )}{2\Gamma (1-x)} = \frac{\Phi\left(-1, 1, -x\right)}{\Gamma(-x)} ...

In mathematics, the '''nu function''' is a generalization of the [[reciprocal gamma function]] of the [[Laplace transform]]. \nu(x) & \equiv \int_0^\infty \frac{x^t \, dt}{\Gamma(t+1)} \\[10pt] ...

{{Short description|Characterization of the gamma function}} ...Wielandt theorem''' [[characterization (mathematics)|characterizes]] the [[gamma function]], defined for all complex numbers <math>z</math> for which <math> ...

...''C''. Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant. Some authors use the phrase "indefinite product" in a slightly different but related way to describe a product in which the numerical value of the upper limit i ...

{{Short description|Contour integral involving a product of gamma functions}} ...irst=Ernest William |last=Barnes|year1=1908|year2=1910}}. They are closely related to [[generalized hypergeometric series]]. ...

...e=A Generalized polygamma function|journal=Integral Transforms and Special Functions|volume=15|issue=2|date=Apr 2004|pages=101–115|doi=10.1080/10652460310001600 It generalizes the [[polygamma function]] to negative and fractional order, but remains equal to it for integer positive orders. ...

...on was found to have applications in the theory of [[fractional calculus]] and also in certain areas of physics.<ref name="Andrea"/> ...In the following definitions, <math>\Gamma (z)</math> is the well known [[gamma function]] defined by ...

| name = Generalized gamma | pdf_image = [[File:GenGamma.png|300px|Gen Gamma PDF plot]] ...

[[Category:Gamma and related functions]] ...

...lassical Eisenstein–Kronecker series, which were studied by Kenichi Bannai and Shinichi Kobayashi using the [[Poincaré bundle]].<ref name="Charollois-Scze ...215/00127094-2010-024 |issn=0012-7094|arxiv=math/0610163 }}</ref> They are related to critical ''L''-values of [[Hecke character]]s.<ref name="BK1"/><ref name ...

...ndall|1996}}, is a function analogous to the [[Riemann zeta function]] and related to the zeros of the [[Airy function]]. [[File:Airy Functions.svg|thumb|The Airy functions Ai and Bi]] ...

...3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New Yo ...the [[q-Hahn polynomials]] ''Q''_''n''(''x'';α,β, ''N'';''q''), and so on. ...

...Prudnikov|authorlink=Anatolii Platonovich Prudnikov}}</ref> It is closely related to the [[Bessel function]]s. ...=Heinrich Friedrich Weber|first=H. F.|last=Weber|year=1879}}, is a closely related function defined by ...

{{Short description|Inverse of the gamma function}} {{Distinguish|Inverse-gamma distribution|Reciprocal gamma function}} ...

...aki1973">{{cite journal | title = Simple derivations of generalized linear and nonlinear Langevin equations | journal = J. Phys. A: Math. Nucl. Gen. | yea ==Slow variables and scalar product== ...

{{Short description|Generalization of the Euler gamma function and the Barnes G-function}} {{For|derivatives of the log of the gamma function |polygamma function}} ...

...sue=3}}</ref> in 2011. The G-MVLG is a flexible distribution. [[Skewness]] and [[kurtosis]] are well controlled by the parameters of the distribution. Thi \prod_{i=1}^k \mu_i \lambda_i^{-\nu-n}}{[\Gamma(\nu+n)]^{k-1}\Gamma(\nu)n!} ...