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Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series

Abstract:

Building on recent work involving the computation of generalizations of Glaisher-type products over the primes by differentiation of the Euler product identity, in the present paper we generalize this approach in order to obtain closed-form expressions of more general infinite products which correspond to Dirichlet series. In this way, we obtain an elegant method to compute a variety of interesting infinite products, and some infinite double products. The Bendersky–Adamchik constants enter in...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s11139-018-0037-4

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
Springer US Publisher's website
Journal:
Ramanujan Journal Journal website
Volume:
49
Issue:
2
Pages:
371–389
Publication date:
2018-08-31
Acceptance date:
2018-05-07
DOI:
EISSN:
1572-9303
ISSN:
1382-4090
Pubs id:
pubs:867612
URN:
uri:6f2a85a6-60c7-4d6c-8299-b6ef3ccafad1
UUID:
uuid:6f2a85a6-60c7-4d6c-8299-b6ef3ccafad1
Local pid:
pubs:867612

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