The generalized modified Bessel function and its connection with Voigt line profile and Humbert functions

Recently Dixit, Kesarwani, and Moll introduced a generalization K<inf>z,w</inf>(x) of the modified Bessel function K<inf>z</inf>(x) and showed that it satisfies an elegant theory similar to that of K<inf>z</inf>(x). In this paper, we show that while [Formula presented] is an elementary function, [Formula presented] 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 η(z). We also establish a connection between [Formula presented] and the cumulative distribution function corresponding to the Voigt line profile.