Evaluation of beta integrals of Ramanujan type and integral representations for bilateral hypergeometric series

In this paper we evaluate integrals of products of gamma functions of Ramanujan type in terms of bilateral hypergeometric series. In cases where the bilateral hypergeometric series are summable, then we evaluate these integral as beta integrals. In addition, we obtain integral representations for bi...

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Vydáno v:The Ramanujan journal Ročník 67; číslo 2; s. 28
Hlavní autoři: Cohl, Howard S., Volkmer, Hans
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Nature B.V 01.06.2025
Témata:
Fourier transforms
Gamma function
Inequality
Integrals
Mathematical functions
Representations
ISSN:1382-4090, 1572-9303
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Shrnutí:In this paper we evaluate integrals of products of gamma functions of Ramanujan type in terms of bilateral hypergeometric series. In cases where the bilateral hypergeometric series are summable, then we evaluate these integral as beta integrals. In addition, we obtain integral representations for bilateral hypergeometric series.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-025-01064-z