Finite summation formulas for the multivariable $A$-function
DOI:
https://doi.org/10.5269/bspm.51894Abstract
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.
References
1. F. Y. Ayant and D. Kumar, Generating relations and multivariable Aleph-function, Analysis 38(3) (2018), 137–143.
2. L. Carlitz, A Saalsch¨utzian theorem for double series, J. London Math. Soc. 38(1) (1963), 415–418.
3. L. Carlitz, A summation for double hypergeometric series, Rend. Sem. Math. Univ. Padova 37 (1967), 230–233.
4. L. Carlitz, Summation of a double hypergeometric series, Matematiche (Catania) 22 (1967), 138–142.
5. 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.
6. 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.
7. B. P. Gautam, A. S. Asgar and A. N. Goyal, On the multivariable A-function, Vijnana Parishad Anusandhan Patrika 29(4) (1986), 67–81.
8. K. C. Gupta and P. K. Mittal, Integrals involving a generalized function of two variables, Indian J. Pure Appl. Math. 5 (1974), 430–437.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
2. L. Carlitz, A Saalsch¨utzian theorem for double series, J. London Math. Soc. 38(1) (1963), 415–418.
3. L. Carlitz, A summation for double hypergeometric series, Rend. Sem. Math. Univ. Padova 37 (1967), 230–233.
4. L. Carlitz, Summation of a double hypergeometric series, Matematiche (Catania) 22 (1967), 138–142.
5. 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.
6. 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.
7. B. P. Gautam, A. S. Asgar and A. N. Goyal, On the multivariable A-function, Vijnana Parishad Anusandhan Patrika 29(4) (1986), 67–81.
8. K. C. Gupta and P. K. Mittal, Integrals involving a generalized function of two variables, Indian J. Pure Appl. Math. 5 (1974), 430–437.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
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2022-12-26
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