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Barnes integral

In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by Ernest William Barnes (1908, 1910). They are closely related to generalized hypergeometric series.

Products, Hypergeometric series & Barnes lemmas

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Overview

Hypergeometric series

Barnes lemmas

Q-Barnes integrals

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Barnes integral

Nodes17
Edges16
Triples14
Avg. degree1.88
Density0.117647
Components1

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Barnes integral

Top relations

related to Hypergeometric series · 9
Barnes integral → Andrews, Askey, Barnes, Given, Roy, Slater, The, Theorem, This
related to q-Barnes integrals · 4
Barnes integral → Barnes, Gasper, Rahman, There
is a · 1
Barnes integral → contour integral involving a product of gamma functions

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Important terminology

hypergeometric barnes integral series functions 1908 isbn mathematics contour 1910 generalized right mr integrals also cambridge university press jfm mellin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Barnes integralis acontour integral involving a product of gamma functions0.90text
Barnes integralrelated to Hypergeometric seriesThe0.60section
Barnes integralrelated to Hypergeometric seriesBarnes0.60section
Barnes integralrelated to Hypergeometric seriesAndrews0.60section
Barnes integralrelated to Hypergeometric seriesAskey0.60section
Barnes integralrelated to Hypergeometric seriesRoy0.60section
Barnes integralrelated to Hypergeometric seriesTheorem0.60section
Barnes integralrelated to Hypergeometric seriesThis0.60section
Barnes integralrelated to Hypergeometric seriesGiven0.60section
Barnes integralrelated to Hypergeometric seriesSlater0.60section
Barnes integralrelated to q-Barnes integralsThere0.60section
Barnes integralrelated to q-Barnes integralsBarnes0.60section

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