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Barnes G-function

In mathematics, the Barnes G-function G ( z ) {\displaystyle G(z)} is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma function.

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Overview

Functional equation and integer arguments

Characterisation

Reflection formula

Taylor series expansion

Asymptotic expansion

Relation to the log-gamma integral

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Barnes G-function

Nodes43
Edges42
Triples25
Avg. degree1.95
Density0.046512
Components1

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Barnes G-function

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related to References · 15
Barnes G-function → Askey, Boisvert, Cambridge University Press, Charles, Clark, Daniel, Frank, ISBN, Lozier, Mathematical Functions, MR, NIST Handbook, Olver, Ronald, Roy
related to Reflection formula · 4
Barnes G-function → Clausen, G-function, Hermann Kinkelin, The
related to Functional equation and integer arguments · 3
Barnes G-function → Euler, Note, The Barnes G-function
related to Relation to the log-gamma integral · 3
Barnes G-function → Digamma, Taking, The

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Important terminology

displaystyle function barnes gamma g-function following constant formula expansion relation kinkelin functional equation integral glaisher terms form reflection multiplication asymptotic

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SubjectPredicateObjectConfidenceSrc
Barnes G-functionrelated to Functional equation and integer argumentsThe Barnes G-function0.60section
Barnes G-functionrelated to Functional equation and integer argumentsNote0.60section
Barnes G-functionrelated to Functional equation and integer argumentsEuler0.60section
Barnes G-functionrelated to ReferencesAskey0.60section
Barnes G-functionrelated to ReferencesRoy0.60section
Barnes G-functionrelated to ReferencesOlver0.60section
Barnes G-functionrelated to ReferencesFrank0.60section
Barnes G-functionrelated to ReferencesLozier0.60section
Barnes G-functionrelated to ReferencesDaniel0.60section
Barnes G-functionrelated to ReferencesBoisvert0.60section
Barnes G-functionrelated to ReferencesRonald0.60section
Barnes G-functionrelated to ReferencesClark0.60section

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