Generalized Coherent States for the Spherical Harmonics $Y_{m}^{m}(\theta,\phi)$

Abstract

The associated Legendre functions $P_{l}^{(m)}(x)$ for a given $l-m$, may be taken into account as the increasing infinite sequences with respect to both indices $l$ and $m$. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics $Y_{m}^{m}(\theta,\phi)$.