Rad HAZU, Matematičke znanosti, Vol. 22 (2018), 107-117.

ON p–EXTENDED MATHIEU SERIES

Tibor K. Pogány and Rakesh K. Parmar

Faculty of Maritime Studies, University of Rijeka, 51 000 Rijeka, Croatia
Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
e-mail: poganj@pfri.hr

Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan State, India
e-mail: rakeshparmar27@gmail.com

Abstract.   Motivated by several generalizations of the well–known Mathieu series, the main object of this paper is to introduce new extension of generalized Mathieu series and to derive various integral representations of such series. Finally, master bounding inequality is established using the newly derived integral expression.

2010 Mathematics Subject Classification.   26D15, 33E20, 44A10, 33C05, 44A20.

Key words and phrases.   Mathieu series, Generalized Mathieu series, Mellin and Laplace transforms, Bessel function of the first kind, Extended Riemann Zeta function.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/90836cwk4y

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