Abstract:
Recently Dixit, Kesarwani, and Moll introduced a generalization of the modified Bessel function and showed that it satisfies an elegant theory similar to that of . In this paper, we show that while is an elementary function, can be written in the form of an infinite series of Humbert functions. As an application of this result, we generalize the transformation formula for the logarithm of the Dedekind eta function . We also establish a connection between and the cumulative distribution function corresponding to the Voigt line profile.