Series representation of the H-function of two variables

Autor: R. K. Saxema y R. U. Verna

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Abstract:

Series representations for the H-function of two variables introduced earlier by Verma[10], are investigated when the poles of the integrand are assumed to be simple. Such representations seem to be non-existent in the literature. Since a number of density functions in a bivariate statistical probability distributions associated with an H-function of one variable are expressible in terms of H-function of two variables, the series representations obtained here would be useful in various problems relating to statistical probability distributions.

Incidentally a special case of one of these series representations gives rise to the series-representation of the generalized Kampe de Feriet’s function, defined and studied by Srivastava and Daoust [ 8 ]and whose convergence conditions are also discussed by them in a subsequent publication [9]. Consequently a general definition of the Srivastava and Daoust function[8] has been obtained in terms of a double Mellin Barnes type integral.

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