Certain Integrals Involving Generalized Multivariable Aleph Function and Wright's Function

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V55P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 2 | Year 2018 | Article Id. IJMTT-V55P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P511

Certain Integrals Involving Generalized Multivariable Aleph Function and Wright's Function

F.Y.Ayant

Abstract

In this paper we define the generalized multivariable Aleph-function in terms of multiple integrals contour. Further we establish certains integrals involving product of the generalized multivariable Aleph-function with exponential function and Fox-Wright's generalized hypergeometric function. Being unified and general nature, these integrals yield a number known and new results as special cases. At the end, we study several corollaries.

Keywords

Generalized multivariable Aleph-function, Mellin-barnes integrals contour, generalized multivariable I-function, Aleph-function, Fox- Wright's generalized hypergeometric function.

References

[1] F.Y. Ayant, An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 31 (3) (2016),142-154.
[2] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[3] C. Fox, The G and H-functions as symmetrical Fourier Kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429.
[4] M. Garg and R. Mishra, On r-dimensional N-fractional differintegral of multivariable H-function, J. Indian Acad. Math, 28 (2006), 189-198.
[5] B.P. Gautam and A.S. Asgar, The A-function. Revista Mathematica. Tucuman (1980).
[6] B.P. Gautam and A.S. Asgar, On the multivariable A-function. Vijnana Parishas Anusandhan Patrika,29(4) (1986), 67-81.
[7] D. Kumar, Generalized fractional differintegral operator of the Aleph-function of two variables, Journal of Chemical, Biological and Physical Sciences (JCBPS), 6(3) (2016), 1116-1131.
[8] A.M. Mathai and R.K. Saxena, The H-function with applications in statistics and other disciplines, John Wiley and Sonc Inc, New York, 1978.
[9] Y.N. Prasad and A.K.Singh, Basic properties of the transform involving and H-function of r-variables as kernel, Indian Acad Math, (2) (1982), 109-115.
[10] E.D. Rainville, Special functions, Chelsea Publishing Co., Bronx, New York, (1971).
[11] V.P. Saxena, Formal solution of certain new pair of dual integral equations involving H-function, Proc. Nat. Acad.Sci. IndiaSect., (2001), A51, 366–375.
[12] K. Sharma, On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences 3(1) ( 2014 ), 1-13.
[13] C.K. Sharma and S.S. Ahmad, On the multivariable I-function. Acta ciencia Indica Math , 20(2) (1994), 113-116.
[14] C.K. Sharma and P.L. Mishra, On the I-function of two variables and its properties. Acta Ciencia Indica Math,17 (1991), 667-672.
[15] H.M. Srivastava, K.C. Gupta and S.P. Goyal, The H-function of one and two variables with applications, South Asian Publisher, New Delhi and Madras (1982).
[16] 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.
[17] H.M.Srivastava and R.Panda, Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25 (1976), 167-197.
[18] N. Südland, B. Baumann and T.F. Nonnenmacher, Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998), 401-402.
[19] N.Sudland, B. Baumann and T.F. Nannenmacher, Fractional drift-less Fokker-Planck equation with power law diffusion coefficients, in V.G. Gangha, E.W. Mayr, W.G. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing (CASC Konstanz 2001), Springer, Berlin, 2001, 513–525.
[20] D.L. Suthar, H. habenom and H Tadesse, Certain integrals involving Aleph-function and Wright's generalized Hypergeometric function, Acta Universitatis Apulensis, no. 52 (2017), 1-10.
[21] E.M. Wright, The asymptotic expansion of the generalized hypergeometric function,Proc. London. Math. Soc. , 46, (1946), 389-408.

Citation :

F.Y.Ayant, "Certain Integrals Involving Generalized Multivariable Aleph Function and Wright's Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 2, pp. 78-88, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P511