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On the functional properties of the confluent hypergeometric zeta-function

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Abstract

A zeta-function associated with Kummer’s confluent hypergeometric function is introduced as a classical Dirichlet series. An integral representation, a transformation formula, and relation formulas between contiguous functions and one generalization of Ramanujan’s formula are given. The inverse Laplace transform of confluent hypergeometric functions is essentially used to derive the integral representation.

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Acknowledgments

The article was written while the author was staying at the Graduate Center of the City University of New York. The author received generous support from this institution.

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Authors and Affiliations

  1. College of Engineering, Nihon University, 1 Nakagawara, Tokusada, Tamuramachi, Kôriyama, Fukushima, 963-8642, Japan

    Takumi Noda

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  1. Takumi Noda
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Correspondence to Takumi Noda.

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Dedicated to the memory of professor Marvin Knopp.

The author was financially supported by Grants-in-Aid for Scientific Research (No. 23540032), Japan Society for the Promotion of Science (JSPS).

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Noda, T. On the functional properties of the confluent hypergeometric zeta-function. Ramanujan J 41, 183–190 (2016). https://doi.org/10.1007/s11139-014-9613-4

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  • DOI: https://doi.org/10.1007/s11139-014-9613-4

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