Some Transformations and Identities for Multivariable Gimel Function

Eulerian integral associated with product of two multivariable A-functions and the classes of polynomials

“…Expressing the multivariable Gimel-function of r-variables and s-variables by the Mellin-Barnes conditions stated). Expressing the multivariable Gimel-function of r-variables and s-variables by the Mellin-Barnes contour integral, see Ayant [2], the generalized hypergeometric function contour integral, see Ayant [2], the generalized hypergeometric function in Mellin-Barnes contour integral with in Mellin-Barnes contour integral with the help of (2.1) and interchange the order of integrations which is justifiable due to absolute convergence of the the help of (2.1) and interchange the order of integrations which is justifiable due to absolute convergence of the integral involved in the process. Now collect the power of integral involved in the process.…”

“…Changing the order of integrations and summation (which is easily seen Mellin-Barnes contour integral. Changing the order of integrations and summation (which is easily seen to be justified due to the absolute convergence of the integral and the summations involved in the process) and to be justified due to the absolute convergence of the integral and the summations involved in the process) and interpreting interpreting Mellin-barnes contour integral to modified multivariable Gimel-function defined by Ayant Mellin-barnes contour integral to modified multivariable Gimel-function defined by Ayant [2] , we obtain the desired result (4.1).…”

“…By the following similar procedure, the results of this document can be extented to product of any finite number of By the following similar procedure, the results of this document can be extented to product of any finite number of multivariable Gimel-functions defined by Ayant [2], multivariable I-function defined by Prathima et al [5] and multivariable Gimel-functions defined by Ayant [2], multivariable I-function defined by Prathima et al [5] and multivariable Aleph-function defined by Ayant. [1] .…”

“…The authors Raina and Srivastava [6], Saigo and Saxena [7], Srivastava and Hussain [11], Srivastava and Garg [10] and other have studied the Eulerian integral. In this paper, we evaluate a new Eulerian integral of most general characters associated with the products of two multivariable Gimel-functions defined by Ayant [2], the expansion of special functions of several variables with general arguments. These functions is an extension of the multivariable H-function defined by Srivastava and Panda [13,14].…”