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Title: Reflection Relation -- from Wolfram MathWorld

Open Graph Title: Reflection Relation -- from Wolfram MathWorld

X Title: Reflection Relation -- from Wolfram MathWorld

Description: A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma function identity Gamma(z)Gamma(1-z)=pi/(sin(piz)), (1) originally discovered by Euler (Havil 2003, pp. 58-59). The reflection relation for the Riemann zeta function zeta(z) is given by zeta(1-z)=chi(z)zeta(z), (2) where chi(z)=2(2pi)^(-z)cos(1/2piz)Gamma(z) (3) and Gamma(z) is the gamma function, as first...

Open Graph Description: A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma function identity Gamma(z)Gamma(1-z)=pi/(sin(piz)), (1) originally discovered by Euler (Havil 2003, pp. 58-59). The reflection relation for the Riemann zeta function zeta(z) is given by zeta(1-z)=chi(z)zeta(z), (2) where chi(z)=2(2pi)^(-z)cos(1/2piz)Gamma(z) (3) and Gamma(z) is the gamma function, as first...

X Description: A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma function identity Gamma(z)Gamma(1-z)=pi/(sin(piz)), (1) originally discovered by Euler (Havil 2003, pp. 58-59). The reflection relation for the Riemann zeta function zeta(z) is given by zeta(1-z)=chi(z)zeta(z), (2) where chi(z)=2(2pi)^(-z)cos(1/2piz)Gamma(z) (3) and Gamma(z) is the gamma function, as first...

Opengraph URL: https://mathworld.wolfram.com/ReflectionRelation.html

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DC.TitleReflection Relation
DC.CreatorWeisstein, Eric W.
DC.DescriptionA reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma function identity Gamma(z)Gamma(1-z)=pi/(sin(piz)), (1) originally discovered by Euler (Havil 2003, pp. 58-59). The reflection relation for the Riemann zeta function zeta(z) is given by zeta(1-z)=chi(z)zeta(z), (2) where chi(z)=2(2pi)^(-z)cos(1/2piz)Gamma(z) (3) and Gamma(z) is the gamma function, as first...
DC.Date.Modified2008-12-31
DC.Subject33
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/ReflectionRelation.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2008-12-31
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