Integral Representation and Asymptotic Expansion for Hypergeometric Coherent States

Abstract

An integral representation is found for hypergeometric coherent states. It contains a generalized hypergeometric function. An asymptotic expansion of hypergeometric coherent states near z=1 is constructed. This expansion is used to find asymptotic eigenfunctions of the Hamiltonian of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters.