Page 318 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics
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Legendre and associated Legendre polynomials         309
                                                             … 1
                                                2l ‡ 1 (l ÿ m)!   m
                                           a lm ˆ               P (ì) f (ì)dì
                                                                  l
                                                  2   (l ‡ m)!  ÿ1
                                                                m
                        The completeness relation for the polynomials P (ì)is
                                                                l
                                         1
                                        X   2l ‡ 1 (l ÿ m)!  m  m
                                                         P (ì)P (ì9) ˆ ä(ì ÿ ì9)
                                                          l
                                                               l
                                              2  (l ‡ m)!
                                        lˆm
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