Solutions of the equation
are called Generalized Associated Legendre Functions. As in the case of (14.21.1), the solutions are hypergeometric functions, and (14.29.1) reduces to (14.21.1) when . For properties see Virchenko and Fedotova (2001) and Braaksma and Meulenbeld (1967).
For inhomogeneous versions of the associated Legendre equation, and properties of their solutions, see Babister (1967, pp. 252–264).