Fractional hypergeometric zeta functions

In this paper we investigate a continuous version of the hypergeometric zeta functions for any positive rational number “ a ” and demonstrate the analytic continuation. The fractional hypergeometric zeta functions are shown to exhibit many properties analogous to its hypergeometric counter part, inc...

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Veröffentlicht in:	The Ramanujan journal 2016-11, Vol.41 (1-3), p.421-436
Hauptverfasser:	Geleta, Hunduma Legesse, Hassen, Abdulkadir
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Hypergeometric functions Mathematics Mathematics and Statistics Number Theory
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Zusammenfassung:	In this paper we investigate a continuous version of the hypergeometric zeta functions for any positive rational number “ a ” and demonstrate the analytic continuation. The fractional hypergeometric zeta functions are shown to exhibit many properties analogous to its hypergeometric counter part, including its intimate connection to Bernoulli numbers.
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-015-9717-5