Operational Calculus in Two Variables and Product of Special Functions

Frederic Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V55P503

International Journal of Mathematics Trends and Technology

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Volume 55 | Number 1 | Year 2018 | Article Id. IJMTT-V55P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P503

Operational Calculus in Two Variables and Product of Special Functions

Frederic Ayant

Abstract

In this paper, we establish few operational relations between the original and the image for two dimensional Laplace transform whose kernel involves the product of the general multivariable polynomials

Keywords

Aleph-function of several variables, A-function, general classes of multivariable polynomials, Bivariate Laplace transform, generalized Lauricella function, Aleph-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] V.B.L. Chaurasia, On simultaneous operational calculus involving a product of Fox's H-function and the multivariable H-function. Jnanabha, 20 (1990), 19-24.
[3] V.B.L. Chaurasia and A. Godika, Operational calculus in two variables and special functions, Indian J. Pure Appl. Math. 31(6) (2000), 675-686.
[4] V.A. Ditkin and A.P. Prudnikov, Operational calculus in two variables and its applications, London Pergamon press (1962).
[5] C. Fox, The G and H-functions as symmetrical Fourier Kernels, Trans. Amer. Math, Soc. 98 (1961), 395-429.
[6] B.P. Gautam and A.S. Asgar. The A-function. Revista Mathematica. Tucuman (1980).
[7] B.P. Gautam and A.S. Asgar, On the multivariable A-function. Vijnana Parishas Anusandhan Patrika, 29(4) (1986), 67-81.
[8] K.S. Kumari, T.M. Vasudevan Nambisan and A.K. Rathie, A study of I-function of two variables, Le Matematiche, 69(1) (2014), 285-305.
[9] Y.N. Prasad, Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 (1986) , 231-237
[10] 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.
[11] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International Journalof Engineering Mathematics Vol (2014), 1-12.
[12] 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.
[13] 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.
[14] C.K. Sharma and S.S. Ahmad, On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, 113- 116.
[15] 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.
[16] H.M. Srivastava, A contour integral involving Fox's H-function. Indian. J. Math, (14) (1972), 1-6.
[17] H.M. Srivastava, A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177 (1985), 183-191.
[18] H.M. Srivastava and M.C. Daoust, Certain generalized Neumann expansions associated with the Kampé de Fériet function. Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math. 31 (1969), 449–457.
[19] H.M. Srivastava and M. Garg, Some integral involving a general class of polynomials and multivariable Hfunction, Rev. Roumaine Phys. 32 (1987), 685-692.
[20] 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.
[21] 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.
[22] 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.
[23] 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.

Citation :

Frederic Ayant, "Operational Calculus in Two Variables and Product of Special Functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 1, pp. 14-23, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P503