Finite Double Integrals Involving Multivariable Gimel-Function

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-61 Number-3
Year of Publication : 2018
Authors : Frédéric Ayant
  10.14445/22315373/IJMTT-V61P523

MLA

MLA Style: Frédéric Ayant "Finite Double Integrals Involving Multivariable Gimel-Function" International Journal of Mathematics Trends and Technology 61.3 (2018): 164-172.

APA Style: Frédéric Ayant (2018). Finite Double Integrals Involving Multivariable Gimel-Function. International Journal of Mathematics Trends and Technology, 61(3), 164-172.

Abstract
In this paper, we establish three finite double integrals involving the multivariable Gimel function with general arguments, general class of polynomials, special functions and Aleph-function. Importance of our findings lies in the fact that they involve the multivariable Gimel function, which are the sufficiently general in nature and are capable of yielding a large number of simpler and useful results merely by specializing the parameters in them. For the sake of illustration, only one particular case of this integral obtained has been given which is also new and is of interest.

References
[1] F. 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] F.Y .Ayant, Some transformations and idendities form multivariable Gimel-function, International Journal of Matematics and Technology (IJMTT), 59(4) (2018), 248-255
[3] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[4] V.B.L.Chaurasia and Y. Singh, New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[5] A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher transcendental function, Vol I (1953).
[6] A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher transcendental function, Vol II (1954).
[7] O.P. Garg, V. Kumar, S.V. Kumar, Some finite double integrals involving general class of polynomials, special functions and multivariable H-function, Math. Ed. (Siwan), 41 (3) (2007), 202-208.
[8] A.M. Mathai and R.K. Saxena, Generalized hypergeometric function with applications in Statistics and physical Sciences, Springer-Verlag Lecture Note no 348, Heidelberg (1973).
[9] Y.N. Prasad, Multivariable I-function , Vijnana Parisha Anusandhan Patrika 29 (1986), 231-237.
[10] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International Journal of Engineering Mathematics Vol (2014), 1-12.
[11] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math. 14(1972), 1-6.
[12] H.M. Srivastava, A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page 183-191.
[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 expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25 (1976), 167-197.
[15] H.M. Srivastava and N.P. Singh, The integration of certains products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo. 32(2)(1983), 157-187.
[16] 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.
[17] N. Südland, B Baumann and T.F. Nonnenmacher, Fractional driftless 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.
[18] V.M. Vyas and R.K. Rathie, An integral involving hypergeometric function, The mathematics education 31(1) (1997), 33.

Keywords
Multivariable Gimel-function, Mellin-Barnes integrals contour , finite double integrals, class of multivariable polynomials, Aleph-function.