On Roots of Apolar Polynomials
In the present paper, we first establish an interesting new chain interconnecting a number of multivariable I-transform of Prathima et al.  by the method of mathematical induction. Full care has been taken of all the convergence and existence conditions for the validity of the chain. The chain established herein has been put in a very compact form and it exhibits an interesting relationship existing between images and originals of a series of related functions in several multidimensional I-function. The importance of our findings lies in the fact that it involves the multivariable I-function which is sufficiently general in nature and so a large number of chains involving other simpler and useful integral transforms of one and more variables follow as special ceses of our chain merely by specializing the parameters. In the end, we shall see several corollaries.
Yua Brychkov H.J. H.J. Glaeske, A.P. Prudnikov and Tuan Vu Kim (1992), Multidimensional integral transformations, Gordan and Breach Science Publisher, Tokyo.
B. L. J. Braaksma, “Asymptotic expansions and analytic continuations for a class of Barnes integrals,” Compositio Mathematical, vol. 15,1964, page. 239–341
S. Cambo, O Marichev and A. Kilbas (1993). Fractional integrals and derivatives, Theory and Applications, Gordan and Breach Science Publisher, Tokyo.
R.S. Garg (1982). On multidimensional Mellin convolutions and H-Transformations, Indian J. Pure Apple. Math.13(1), 30-38.
K.C. Gupta Rashmi Jain and Rashmi Garg, On a chain involving the multivariable H-transform, Proc. Int. Conf.SSFA, 2( 2001), 147-159.
J. Prathima, V. Nambisan S.K. and Kurumujji, A Study of I-function of Several Complex Variables, International Journal of Engineering Mathematics Vol (2014), 1-12.
A.K.Rathie, A new generalization of generalized hypergeometric functions, Le matematiche 52 (2) (1997), 297-310.
H.M. Srivastava, K.C. Gupta and S.P. Goyal (1982). The H-function of one and two variables with applications, South Asian Publishers, New Delhi.
H.M. Srivastava and R. Panda (1978). Certain multidimensional integral transformations (I) and (II), Nederl. Akad. Wedensch.Proc.Ser. A81, 118-144.
Copyright (c) 2019 Frédéric Ayant, Dr Gulshan Chand Gupta, Dr. Vinod Gill
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