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

Author

Listed:
  • 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
    Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia)

  • S. Saravanan

    (Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry 605014, India)

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.

Suggested Citation

  • Rakesh K. Parmar & Tibor K. Pogány & S. Saravanan, 2023. "On Mathieu-Type Series with ( p , ν )-Extended Hypergeometric Terms: Integral Representations and Upper Bounds," Mathematics, MDPI, vol. 11(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1710-:d:1114823
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