Finite Integral Involving the Modified Generalized I-Function of Two Variables, Generalized Extented Hurwitz’s Zeta Function of Two Variables and Exponential Function

Authors

  • Frédéric Ayant Teacher in High School, FRANCE

DOI:

https://doi.org/10.31033/ijrasb.9.1.1

Keywords:

Modified generalized I-function of two variables, generalized I-function of two variables, generalized modified H-function of two variables, generalized modified Meijer-function of two variables, I-function of two variables, H-function of two variables, Meijer-function of two variables, double Mellin-Barnes integrals contour, finite integral, generalized extented Hurwitz’s Zeta function of two variables

Abstract

In the present paper, we evaluate the general finite integral involving the exponential function, generalized Hurwitz’s-Lerch zeta function of two variables and the modified of generalized I-function of two variables. At the end, we shall see several corollaries and remarks.

Downloads

Download data is not yet available.

References

R.P. Agarwal, "An extension of Meijer's G-function," Proc. Nat. Inst. Sci. India Part A, 31 (1965), 536-546.

M.K. Bansal and D. Kumar, On the integral operators pertaining to a family of incomplete I-functions, AIM Mathematics 5(2) (2020), 1247-1259.

M.K. Bansal, D. Kumar, K.S. Nisar and J. Singh, Certain fractional calculus and integral transform results of incomplete Aleph-functions with applications, Math. Mech; Appli. Sci (Wiley), (2020), 1-13.

M.K. Bansal, D. Kumar, I. Khan, J. Singh and K.S. Nisar, Certain unified integrals associated with product of Mseries and incomplete H-functions, Mathematics, (7) (2019), 1-11.

G. Maged G. Bin-Saad and Amani M. Hanballa, On hypergeometric series associated with the generalized zeta functions, SCIREA Journal of Mathematics 1 (2016), 53-62.

Maged G. Bin-Saad, M. A. Pathan and Ali Z. Bin-Alhag, On multiple zeta function and associated properties, Turkish Journal of Analysis and Number Theory 6 (2018), 84-89

B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.

Y.A. Brychkov, Handbook of special functions, Derivatives, Integrals, Series and oher formulas, CRC. Press. Taylor and Francis Group. Boca. Raton, London, New York 2008.

A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill Book Inc., New York, Toronto and London, 1953.

H. Exton, A note on a hypergeometric transformation, Bull. Calcutta Math. Soc. 71 (1979), 337-340.

H. Exton, Reducible double hypergeometric functions and associated integrals, An. Fac. Ci. Univ. Porto 63(1-4) (1982), 137-143.

K.C. Gupta, and P.K. Mittal, Integrals involving a generalized function of two variables, (1972), 430-437.

D. Kumar, Generalized fractional differintegral operators of the Aleph-function of two variables, Journal of Chemical, Biological and Physical Sciences, Section C, 6(3) (2016), 1116-1131.

K S. Kumari, T.M. Vasudevan Nambisan and A.K. Rathie, A study of I-functions of two variables, Le matematiche 69(1) (2014), 285-305.

M. A. Pathan and O. Daman, On Generalization of Hurwitz zeta function, Non-Linear World Journal, (2018), to appear.

M. A. Pathan, Maged G. Bin-Saad and J. A. Younis, Hurwitz Zeta Function of Two Variables and Associated Properties, Earthline Journal of Mathematical Sciences, Vol 3 (2), (2020), 297-315.

Y. Pragathi Kumar and B. Satyanarayana, A study of Psi-function, Journal of Informatics and mathematical Sciences, Vol. 12 (2) (2020), 159-171.

Y.N. Prasad and S. Prasad, (1979 -1980): Journal of scientific research, Banaras Hindu University, 30 (1), 67 -76.

A.K. Rathie, A new generalization of generalized hypergeometric functions, Le matematiche 52 (2) (1997), 297-310.

V.P. Saxena, The I-function, Anamaya Publishers, New Delhi, 2008.

K. Sharma, On the Integral Representation and Applications of the Generalized Function of Two Variables, International Journal of Mathematical Engineering and Science, 3(1) (2014), 1-13.

H. Singh and P. Kumar, Finite integral formulas involving multivariable Mittag-Leffler function and Modified I function, Int. Jr. of Mathematical sciences and Application, Vol 8(2), (2018), 115-128.

H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associate Series and Integrals, Elsevier Science, Publishers, Amsterdam, London and New York, 2012.

H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. 12 (1976), 419-425.

H. M. Srivastava and M. A. Pathan, Some bilateral generating functions for the extended Jacobi polynomials, Comment. Math. Uni. St. Paul 28(1) (1979), 23-30.

N. Südland, N B. Baumann and T.F. Nonnenmacher, Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): 401-402

Downloads

Published

2022-01-31

How to Cite

Ayant, F. . (2022). Finite Integral Involving the Modified Generalized I-Function of Two Variables, Generalized Extented Hurwitz’s Zeta Function of Two Variables and Exponential Function. International Journal for Research in Applied Sciences and Biotechnology, 9(1), 1–14. https://doi.org/10.31033/ijrasb.9.1.1