Finite summation formulas for the multivariable $A$-function
Abstract
The object of this paper is to evaluate some finite double summations relations for the multivariable $A$-function using the summation of a double hypergeometric series. The formulas derived in this paper are most general in character, we also provide a few particular cases for derived summation formulas.
Downloads
References
F. Y. Ayant and D. Kumar, Generating relations and multivariable Aleph-function, Analysis 38(3) (2018), 137–143. DOI: https://doi.org/10.1515/anly-2017-0054
L. Carlitz, A Saalsch¨utzian theorem for double series, J. London Math. Soc. 38(1) (1963), 415–418. DOI: https://doi.org/10.1112/jlms/s1-38.1.415
L. Carlitz, A summation for double hypergeometric series, Rend. Sem. Math. Univ. Padova 37 (1967), 230–233.
L. Carlitz, Summation of a double hypergeometric series, Matematiche (Catania) 22 (1967), 138–142.
J. Choi, J. Daiya, D. Kumar and R.K. Saxena, Fractional differentiation of the product of Appell function F3 and multivariable H-function, Commun. Korean Math. Soc. 31(1) (2016), 115–129. DOI: https://doi.org/10.4134/CKMS.2016.31.1.115
J. Daiya, J. Ram and D. Kumar, The Multivariable H-function and the general class of Srivastava polynomials involving the generalized Mellin-Barnes contour integrals, Filomat 30(6) (2016), 1457–1464. DOI: https://doi.org/10.2298/FIL1606457D
B. P. Gautam, A. S. Asgar and A. N. Goyal, On the multivariable A-function, Vijnana Parishad Anusandhan Patrika 29(4) (1986), 67–81.
K. C. Gupta and P. K. Mittal, Integrals involving a generalized function of two variables, Indian J. Pure Appl. Math. 5 (1974), 430–437.
D. Kumar, F. Y. Ayant and J. Choi, Application of product of the multivariable A-function and the multivariable Srivastava polynomials, East Asian Math. J. 34(3) (2018), 295–303.
D. Kumar, F. Y. Ayant and D. Kumar, A new class of integrals involving generalized hypergeometric function and multivariable Aleph-function, Kragujev. J. Math. 44(4) (2020), 539–550. DOI: https://doi.org/10.46793/KgJMat2004.539K
D. Kumar, S. D. Purohit and J. Choi, Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials, J. Nonlinear Sci. Appl. 9(1) (2016), 8–21. DOI: https://doi.org/10.22436/jnsa.009.01.02
J. Ram and D. Kumar, Generalized fractional integration involving Appell hypergeometric of the product of two H-functions, Vijanana Parishad Anusandhan Patrika 54(3) (2011), 33–43.
H. M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables, Comment. Math. Univ. St. Paul. 24 (1975), 119–137.
H. M. Srivastava and R. Panda, Some bilateral generating function for a class of generalized hypergeometric polynomials, J. Reine Angew. Math. 283/284 (1976), 265–274. DOI: https://doi.org/10.1515/crll.1976.283-284.265
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
