On the Barnes double gamma function

On the Barnes double gamma function

We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function . Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic ex...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 34; no. 12; pp. 891 - 914
Main Authors: Alexanian, S., Kuznetsov, A.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02-12-2023
Taylor & Francis Ltd
Subjects:
Algorithms
asymptotic expansion
Asymptotic series
Barnes double gamma function
Bernoulli numbers
Gamma function
Primary 33B15
Product differentiation
Secondary 30E15
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Summary:We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function . Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as . Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms and .
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2023.2238115