Title: An Integral Formula Generated by Hurwitz-Lerch Zeta Function with Order 1
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-20-00029; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 12-16
Document Type: Research Paper
Author(s): Aykut Ahmet Aygunes a
Received: 13 September 2020, Accepted: 21 October 2020, Published: 25 April 2021.
Corresponding Author: Aykut Ahmet Aygunes (Email address: firstname.lastname@example.org)
Full Text: PDF
In this paper, we give some results associated with Hurwitz-Lerch zeta function with order 1 which is special case of Hurwitz-Lerch zeta function. One of the results is the integral formula including Hurwitz-Lerch zeta function with order 1. The other result is a corollary generated by integral representation of Hurwitz-Lerch zeta function with order 1.
Keywords: Hurwitz-Lerch zeta function, Hurwitz-Lerch zeta function with order 1, Riemann zeta functionReferences:
- A. A. Aygunes, Some identities for a special case of Hurwitz-Lerch zeta function, Numerical Analy. Appl. Math. AIP Conf. Proc. 1863 (1), 300018, 2016.
- A. A. Aygunes, Hurwitz-Lerch zeta function with order 1, J. Math. Sci. 1, 16-24, 2017.
- A. Erdélyi, Higher Transcendental Functions, vol. 1, McGrow-Hill, New York, 1955.
- A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, vol. 1, McGraw-Hill Book Company, New York, Toronto and London, 1953.
- E. C. Titchmarsh, The Theory of the Riemann-zeta function, Oxford University (Clarendon) Press, Oxford and London, 1951; Second Edition (Revised by D. R. Heath-Brown), 1986.
- H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
- H. M. Srivastava, Some properties and results involving the zeta and associated functions, Functional Analysis, Approximation and Computation 7 (2), 89-133, 2015.
- J. Choi, Remark on the Hurwitz-Lerch zeta function, Fixed Point Theory and Applications 70, 2-10, 2013.
- L. Lewin, Polylogarithms and Associated Functions, North-Holland, New York, 1981.
- T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, Heidelberg and Berlin, 1976.