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Title: Incomplete Gamma Function -- from Wolfram MathWorld

Open Graph Title: Incomplete Gamma Function -- from Wolfram MathWorld

X Title: Incomplete Gamma Function -- from Wolfram MathWorld

Description: The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is given by Gamma(a,x)=int_x^inftyt^(a-1)e^(-t)dt. (1) For a an integer n Gamma(n,x) = (n-1)!e^(-x)sum_(k=0)^(n-1)(x^k)/(k!) (2) = (n-1)!e^(-x)e_(n-1)(x), (3) where e_n(x) is the exponential sum function. It is implemented as Gamma[a, z] in the Wolfram Language. The special case of x=-1 can be...

Open Graph Description: The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is given by Gamma(a,x)=int_x^inftyt^(a-1)e^(-t)dt. (1) For a an integer n Gamma(n,x) = (n-1)!e^(-x)sum_(k=0)^(n-1)(x^k)/(k!) (2) = (n-1)!e^(-x)e_(n-1)(x), (3) where e_n(x) is the exponential sum function. It is implemented as Gamma[a, z] in the Wolfram Language. The special case of x=-1 can be...

X Description: The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is given by Gamma(a,x)=int_x^inftyt^(a-1)e^(-t)dt. (1) For a an integer n Gamma(n,x) = (n-1)!e^(-x)sum_(k=0)^(n-1)(x^k)/(k!) (2) = (n-1)!e^(-x)e_(n-1)(x), (3) where e_n(x) is the exponential sum function. It is implemented as Gamma[a, z] in the Wolfram Language. The special case of x=-1 can be...

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DC.TitleIncomplete Gamma Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionThe "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is given by Gamma(a,x)=int_x^inftyt^(a-1)e^(-t)dt. (1) For a an integer n Gamma(n,x) = (n-1)!e^(-x)sum_(k=0)^(n-1)(x^k)/(k!) (2) = (n-1)!e^(-x)e_(n-1)(x), (3) where e_n(x) is the exponential sum function. It is implemented as Gamma[a, z] in the Wolfram Language. The special case of x=-1 can be...
DC.Date.Modified2019-03-14
DC.Subject33B15
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/IncompleteGammaFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2019-03-14
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og:typewebsite
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