  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 $Y_{m}^{m}(\theta,\phi)$.
