On Mathieu-Type Series with ( p, ν )-Extended Hypergeometric Terms: Integral Representations and Upper Bounds

Rakesh K. Parmar, Tibor K. Pogány () and S. Saravanan
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Rakesh K. Parmar: Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry 605014, India
Tibor K. Pogány: Institute of Applied Mathematics, John von Neumann Faculty of Informatics, Óbuda University, Bécsi út 96/b, 1034 Budapest, Hungary
S. Saravanan: Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry 605014, India

Mathematics, 2023, vol. 11, issue 7, 1-11

Abstract: Integral form expressions are obtained for the Mathieu-type series and for their associated alternating versions, the terms of which contain a ( p , ν ) -extended Gauss hypergeometric function. Contiguous recurrence relations are found for the Mathieu-type series with respect to two parameters, and finally, particular cases and related bounding inequalities are established.

Keywords: ( p , ? )-extended Beta function; ( p , ? )-extended Gauss hypergeometric function; ( p , ? )-extended confluent hypergeometric function; ( p , ? )-extended Mathieu-type series; modified Bessel function of the second kind; bounding inequalities for ( p , ? )-extended Mathieu-type series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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