sentences:  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 formula_2 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 formula_4 is the Gamma function.