Abstract

The function Jm,n(x) has been called by Humbert a Bessel function of the third kind, but in order to avoid confusion with the ordinary Bessel function of the third kind, I shall call it a Humbert function. The object of this paper is to investigate' some properties of Humbert functions so far as the convergence of infinite series involving the functions are concerned. In general we can have the following two types of infinite series involving the functions:

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