Certain properties of Mathieu-type series associated with hypergeometric functions
Résumé
The objective of current article is to investigate some properties of Mathieu-type series and with their alternating version as kernel Gauss hypergeometric function. Also we discussed some particular cases of the result obtained here.
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Références
Pogany, T.K., Integral representation of a series which includes the Mathieu a-series, J. Math. Anal. Appl.,2004, 296 , 309—313.
Cahen, E. , Sur la fonction ζ(s) de Riemann et sur des fontions analogues, Ann. Sci. l’Ecole Norm. Sup. Ser. Math., 1894, 75-–164.
Pogany, T.K. and Tomovski, Z, On Mathieu-type series which terms contain general- ized hypergeometric function pFq and Meijer’s G-function, Math. Comput. Modell., 2008, 47, 9-10, 952—969.
Baricz, A, Butzer, P.L. Butzer, Pogany T.K. , Alternating Mathieu series, Hilbert-Eisenstein series and their generalized Omega functions, in T. Rassias, G. V. Milovanovic (Eds.), Analytic Number Theory, Approximation Theory, and Special Functions - In Honor of Hari M. Srivastava, 775, Springer, New York, 2014.
Pogany, T.K., Integral representation of Mathieu (a, λ)-series, Integral Transforms Spec. Funct.,2005, 16,8, 685—689.
Pogany,T.K.and H.M. Srivastava, Some Mathieu-type series associated with the Fox- Wright function, Comput. Math. Appl., 2009, 57, 1, 127-–140.
Jain, S.; Goyal, R.; Agarwal, P.; Lupica, A.; Cesarano, C. Some results of extended beta function and hypergeometric functions by using Wiman’s function, Mathemtics 2021, 9(22), 2944.
Goyal, R.; Agarwal, P.; Momami, S.; Rassias, M.T. An Extension of Beta Function by Using wiman’s function. Axioms, 2021,10, 187.
Wiman, A. U ber der Fundamentalsatz in der Theorie der Funktionen Eα(x). Acta Math. 1905, 29, 191-201.
Shadab, M.S.; Jabee, S.J.; Choi, J.C. An extended Beta function and its applications, Far East J. Math. Sci. (FJMS) 2018, 103, 235–251.
Chaudhry, M.A.; Qadir, A.; Srivastava, H.M.; Paris, R.B. Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 2004, 159, 589–602.
Olver, W.J.F.; Lozier, W.D.; Boisvert, F.R.; Clark, W.C.,NIST Handbook of Mathematical Functions ; Cambridge University Press, New York, NY, USA, 2010.
Rainville, E.D., Special Functions; Macmillan: New York, NY, USA, 1960.
Nathwani, B. V., Dave, B. I.; Generalized Mittag-Leffler function and its properties, The Mathematics student Journal, 2017, 86(1-2), 63–76.
Nathwani, B. V.; Inequalities involving Mittag-Leffler type q-Konhauser polynomial, Studia Universitatis Babes-Bolyai Mathematica, 2020, 65(3), 379–401.
Prajapati, J. C., Dave, B. I., Nathwani, B. V.; On a unification of generalized Mittag-Leffler function and family of Bessel functions, Advances in Pure Mathematics, 2013, 3, 127–137.
Prajapati, J. C., Nathwani, B. V.; Fractional calculus of a unified Mittag-Leffler function, Ukrainian Mathematical Journal, 2015, 66(8), 1267–1280.
Sanjhira, R. R., Nathwani, B. V., Dave, B. I.; Generalized Mittag-Leffler matrix function and associated matrix polynomials, The Journal of the Indian Mathematical Society, 2019, 86(1-2), 161–178.
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