The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals

Abdi Oli; Kelelaw Tilahun; G. V. Reddy

doi:10.4067/S0719-06462020000300351

DOI:

https://doi.org/10.4067/S0719-06462020000300351

Abstract

In this paper, we have evaluated three definite integrals involving the product of two hypergeometric functions and multivariable Aleph-function. Certain special cases of the main results are also pointed out.

Keywords

Hypergeometric function , Multivariable Aleph function

Abdi Oli Department of Mathematics, Wollo University, P.O. Box: 1145, Dessie, South Wollo, Amhara Region, Ethiopia.
Kelelaw Tilahun Department of Mathematics, Wollo University, P.O. Box: 1145, Dessie, South Wollo, Amhara Region, Ethiopia.
G. V. Reddy Department of Mathematics, Jigjiga University, P.O. Box: 1020, Jigjiga, Ethiopia.

Pages: 351–359
Date Published: 2020-12-07
Vol. 22 No. 3 (2020)

M. Chand, “New Theorems involving the I-function and general class of polynomials”, Global Journal of science Frontier Research, vol. 12, no 4-F, 56–68, 2012.

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, vol. 30, no. 6, 1457–1464, 2016.

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., vol. 9, 8–21, 2016.

Y. N. Prasad, “Multivariable I-function, Vijñãna Parishad Anusandhan Patrika”, vol. 29, no. 4, 231–235, 1986.

M. I. Qureshi, K.A. Quraishi and R. Pal, “Some definite integrals of Gradshteyn-Ryzhil and other integrals”, Global Journal of Science Frontier Research, vol. 11, no. 4, 75–80, 2011.

C. K. Sharma and S.S. Ahmad, “On the multivariable I-function”. Acta ciencia Indica Math, vol. 20, no. 2, 113–116, 1994.

C. K. Sharma and G.K. Mishra, “Exponential Fourier series for the multivariable I-function”, Acta Ciencia Indica Mathematics, vol. 21, no. 4, 495–501, 1995.

L. J. Slater, “Generalized Hypergeometric functions”, Cambridge Univ. Press, Cambridge, London and New York, (1996).

R. K. Saxena, J. Ram and D.L. Suthar, “Unified fractional derivative formulas for the multi- variable H-function”, Vijnana Parishad Anusandhan Patrika, vol. 49, no. 2, (2006), 159–175, 2006.

H. M. Srivastava, R. Panda, “Some expansion theorems and generating relationsfor the H-function of several complex variables”, Comment. Math. Univ. St. Paul. vol. 24, 119–137, 1975.

N. Sudland, B. Baumann and T. F. Nonnenmacher, “Open problem: who knows about the Aleph-function?”, Fract. Calc. Appl. Anal., vol. 1, no. 4, 401–402, 1998.

D. L. Suthar and P. Agarwal, “Generalized Mittag-Leffler function and the multivariable H-function involving the Generalized Mellin-Barnes contour integrals”, Communications in Numerical Analysis, vol. 1, 25–33, 2017.

D. L. Suthar, B. Debalkie, and M. Andualem, “Modified Saigo fractional integral operators involving multivariable H-function and general class of multivariable polynomials”, Advances in Difference Equation, vol. 213, 2019. DOI: 10.1186/s13662-019-2150-0.

D. L. Suthar, H. Habenom and H. Tadesse, “Certain integrals involving Aleph function and Wright‘s generalized Hypergeometric function”, Acta Universitatis Apulensis, vol. 52, 1–10, 2017.

D. L. Suthar, S. Agarwal and D. Kumar, “Certain integrals involving the product of Gaussian hypergeometric function and Aleph function”. Honam Mathematical J., vol. 41, no. 1, (2019), 1–17, 2019.

D. L. Suthar and B. Debalkie, “A new class of integral relation involving Aleph-functions”, Surveys in Mathematics and its Applications, vol. 12, 193–201, 2017.