Heine's identity


In mathematical analysis, Heine's identity, named after Heinrich Eduard Heine is a Fourier expansion of a reciprocal square root which Heine presented as
where is a Legendre function of the second kind, which has degree, m − 1/2, a half-integer, and argument, z, real and greater than one. This expression can be generalized for arbitrary half-integer powers as follows
where is the Gamma function.