Some q-Hypergeometric representations of the multiple Hurwitz zeta function

Fadhl S. N. Alsarahi; Fadhle B.F.Mohsen

Fadhl S. N. Alsarahi Department of Mathematics, Faculty of Education, Aden University, Aden, Yemen
Fadhle B.F.Mohsen Department of Mathematics, Faculty of Education, Aden University, Aden, Yemen

Keywords: multiple Hurwitz zeta function, q-Hypergeometric series, q-shifted factorial and special function.

Abstract

In this paper, The main object to give some new representations of the q-analogue of the multiple Hurwitz zeta function are derived.

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References

Barnes, E.W., The theory of the G-function, Quart.J.Math,31(1899), 264-314.

Barnes, E.W., Genesis of the double Gamma function, Proc. London Math. Soc., (sec.1), 31(1900), 358-381.

Barnes, E.W., The theory of the double Gamma function, Philes. Trans. Roy. Sec. London ser.A, 196(1901),265-388.

Barnes, E.W., The theory of the multiple Gamma functions, Trans. Combridge Philos. Soc., 19(1904),374-439.

Ernst, T., A new method for q-hypergeometric series and a new q-Taylor formula. Uppsala. (2000).

Ernst, T., A method for q-calculus, J. of Nonlinear mathematical physics, Vol. 10, No.4, pp487-525, 2003.

Ernst, T., q-calculus as operational algebra, Proceedings of the Estonian Academy of sciences vol. 58, No.2, pp73-97, 2009.

Gasper,G. and Rahman, M., Basic hypergemetric series, Cambridge university Press, 2004.

Kim, T., Non-archimedead q-integrals associated with multiple Chunghee qBernoulli polynomials, Bass. J. Math phys., 10(2003) 91-98.

Kim, T., Analytic continuation of multiple q-zeta functions and their values at negative integers, Bass. J. Math phys., 11(2004) 71-76.

Koekoek, R. and Swarttouw, R.F., The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report 98-17, Faculty of Technical mathematics and informatics, Delft university, 1998.

Michitomo, N., Generalization of Gamma function and its applications to q-analysis.

Soria-Lorente,A., Cumbrera-Gonzalez,B., q-hypergeometric representations of the q-analogue of zeta function, Journal of Fractional Calculus and Applications, Vol. 5(2), July 2014, pp.1-8.

Soria-Lorente,A., Some q-representations of the q-analogue of Hurwitz zeta function, Lecturas Matema'ticas, Vol. 36(1), 2015, pp.12-22.