H τ1,τ2,τ3 B Srivastava Hypergeometric Functio

Year 2019, Volume: 7 Issue: 2, 195 - 204, 15.10.2019

Oğuz Yağcı

https://doi.org/10.36753/mathenot.634502

Cited By: 1

Abstract

Formulas and identities involving many well known special functions (such as the Gamma and Beta functions, Gauss hypergeometric function, and so on) play important roles in themselves and their diverse applications. In this paper, we will add τ1, τ2, τ3 parameters to the HB Srivastava hypergeometric function and we introduce new H τ1,τ2,τ3 B Srivastava’s triple τ -hypergeometric function. Then, we present some properties of the H τ1,τ2,τ3 B Srivastava’s triple τ -hypergeometric function.

Keywords

Srivastava hypergeometric function, Integral representations, Recurrence relations

References

• \bibitem{1} Agarwal, P., Some inequalities involving Hadamard‐type k‐fractional integral operators. Mathematical Methods in the Applied Sciences, (2017), no.40(11), 3882--3891. \bibitem{2} Agarwal, P., Jleli, M. and Tomar, M., Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals. Journal of inequalities and applications, (2017), no.1, 55. \bibitem{3} Agarwal, P., Tariboon, J. and Ntouyas, S. K., Some generalized Riemann-Liouville k-fractional integral inequalities. Journal of Inequalities and Applications, (2016), no.1, 122. \bibitem{4} Al-Shammery, A. H., and Kalla,Shyam. L., An extension of some hypergeometric functions of two variables. Revista de la Academia Canaria de Ciencias 12 (2000),no.2, 189-196. \bibitem{5} Appell,P., Kamp\'{e} de F\'{e}riet, Fonctions Hyperg\'{e}om\'{e}triques et Hypersph\'{e}riques. Gauthier-Villars, Paris, (1926). \bibitem{6} Baleanu, D. and Agarwal, P., Certain inequalities involving the fractional-integral operators. In Abstract and Applied Analysis (2014), Hindawi. \bibitem{7} Baleanu, D., Purohit, S. D. and Agarwal, P., On fractional integral inequalities involving hypergeometric operators. Chinese Journal of Mathematics, (2014). \bibitem{8} Choi, J. and Agarwal, P., A note on fractional integral operator associated with multiindex Mittag-Leffler functions. Filomat, (2016), no.30(7), 1931--1939. \bibitem{9} Choi, J. and Agarwal, P., Some new Saigo type fractional integral inequalities and their-analogues. In Abstract and Applied Analysis (2014) Hindawi. \bibitem{10} Choi, J., Parmar,Rakesh K. and Chopra,P., The incomplete Lauricella and first Appell functions and associated properties. Honam Mathematical Journal (2014),no.3, 531-542. \bibitem{11} \c{C}etinkaya, A.,Ya\u{g}basan, M.Baki. and K\i ymaz,\.{I}.Onur., The extended Srivastava's hypergeometric function and their integral representation. J. Nonlinear sci. Appl. (2016),no.9, 4860-4866. \bibitem{12} Exton, H., On Srivastava's symmetrical triple hypergeometric function $H_{B}$. J. Indian Acad. Math. (2003),no.25, 17-22. \bibitem{13} Hasanov, A., Srivastava, Hari. M. and Turaev, M., Integral representation of Srivastava's triple hypergeometric function.Taiwanese Journal of Mathematics (2011),no.6,2751-2762. \bibitem{14} Opps, Sheldon.B., Saad, N. and Srivastava, Hari. M., Some reduction and transformation formulas for the Appell hypergeometric function\textit{\ }$ F_{2}$. J. Math. Anal. Appl. (2005),no.1 180-195. \bibitem{15} Opps, Sheldon. B., Saad, N. and Srivastava, Hari. M., Recursion formulas for Appell's hypergeometric function $F_{2}$\ with some applications to radiation field problem. Appl. Math. Comput. (2009),no.2, 545-558. \bibitem{16} Parmar, Rakesh K., Extended hypergeometric functions and associated properties. C. R. Math. Acad. Sci. Paris (2015),no.5, 421-426. \bibitem{17} Parmar, Rakesh K. and Saxena,Ram Kishore., The incomplete generalized $\tau -$ hypergeometric and second $\tau -$Appell functions. Journal of the Korean Mathematical Society (2016),no.2 363-379. \bibitem{18} Rainville, Earl. D., Special functions. Macmillan Company, New York,1960. Reprinted by Chelsea Publishing Company, Bronx, New York, 1971. \bibitem{19} Ruzhansky, M., Cho, Y. J., Agarwal, P. and Area, I. (Eds.)., Advances in real and complex analysis with applications. Springer Singapore (2017). \bibitem{20} Slater, Lucy. J., Generalized Hypergeometric Functions. Cambridge University Press. Cambridge, 1966. \bibitem{21} Srivastava, Hari. M., Hypergeometric functions of three variables.Ganita 15 (1964),no.2, 97-108. \bibitem{22} Srivastava, Hari. M. and Karlsson, Per. W., Multiple Gaussian Hypergeometric Series. Halsted Press (John Wiley and Sons), New York, 1985. \bibitem{23} Srivastava, Hari. M. and Monacha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane and Toronto, 1984. \bibitem{24} Srivastava, Hari. M., Some integrals representing triple hypergeometric functions . Rend. Circ. Mat. Palermo, (1967),no.2, 99-115. \bibitem{25} Srivastava, Hari. M., Relations between functions contiguous tocertain hypergeometric functions of three variables. Proc. Nat. Acad. Sci.India Sect. A, 36 (1966),no.1, 377-385. \bibitem{26} \c{S}ahin, R., Recursion Formulas for Srivastava Hypergeometric Functions. Mathematica Slovaca, 65 (2015), no:6, 1345-1360. \bibitem{27} \c{S}ahin, R. and Yağcı, O., $H_{A}^{\tau_{1}, \tau_{2}, \tau_{3}}$ Srivastava Hypergeometric Function, Mathematical Sciences and Applications E-Notes, (2018), no.6(2), 1-9. \bibitem{28} Tariboon, J., Ntouyas, S. K. and Agarwal, P., New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations. Advances in Difference Equations, (2015), no.1, 18. \bibitem{29} Wang, G., Agarwal, P. and Chand, M., Certain Grüss type inequalities involving the generalized fractional integral operator. Journal of Inequalities and Applications, (2014), no.1, 147. \bibitem{30} Virchenko,N., Kalla, Shyam. L. and Al-Zamel,A., Some results on a generalized hypergeometric function. Integral Transforms and Special Functions (2001),no.1, 89-100. \bibitem{31} Virchenko,N., On some generalizations of the functions of hypergeometric type. Fract. Calc. Appl. Anal. (1999), no. 3, 233-244. \bibitem{32} Zhang, X., Agarwal, P., Liu, Z. and Peng, H., The general solution for impulsive differential equations with Riemann-Liouville fractional-order $q\in(1,2)$. Open Mathematics, (2015), no.1, 13.