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Plana's summation formula as a modular relation and applications.
- Source :
-
Integral Transforms & Special Functions . Mar2012, Vol. 23 Issue 3, p183-190. 8p. - Publication Year :
- 2012
-
Abstract
- In this paper, we shall locate Plana's summation formula à la Koshlyakov as a form of the modular relation for the Riemann zeta-function and an analytic continuation technique furnished by Lemma 1. Then by Plana's summation formula, we shall prove an important integral representation for the Hurwitz–Lerch zeta-function through confluent hypergeometric functions, which cover a wide range of integral representations attributed to famous mathematicians. We shall also locate the genesis of Mikolás’ formula and prove that the functional equations for the Hurwitz zeta-function and the Riemann zeta-function are equivalent. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 10652469
- Volume :
- 23
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Integral Transforms & Special Functions
- Publication Type :
- Academic Journal
- Accession number :
- 71861087
- Full Text :
- https://doi.org/10.1080/10652469.2011.574848