Derivatives with respect to the degree and order of associated Legendre functions for $|z|>1$ using modified Bessel functions.

link: http://arxiv.org/abs/0911.5266
Abstract

Expressions for the derivatives with respect to order of modified Bessel
functions evaluated at integer orders and certain integral representations of
associated Legendre functions with modulus argument greater than unity are used
to compute derivatives of the associated Legendre functions with respect to
their parameters. For the associated Legendre functions of the first and second
kind, derivatives with respect to the degree are evaluated at odd-half-integer
degrees, for general complex orders, and derivatives with respect to the order
are evaluated at integer orders, for general complex degrees.