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 followswhere is the Gamma function.
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