※ 引述《Frobenius (▽．(▽×▽φ)=0)》之銘言：
: Show that
:                                  n-s
:                  (s - n)!     (-1)  (2n - 2s)!
:                ────── = ────────
:                 (2s - 2n)!        (n - s)!
: Here s and n are integers with s < n. This result can be used to avoid
: negative factorials such as in the series representations of the spherical
: Neumann funtions and the Legendre functions of the second kind.
(s-n)! = (s-n)(s-n-1)!
       = (s-n)(s-n-1)...(2s-2n+1)(2s-2n)!

(s-n)!/(2s-2n)! = (-1)^(n-s) (n-s)(n+1-s)...(2n-1-2s)
                = (-1)^(n-s) (2n-1-2s)!/(n-s-1)!
                = (-1)^(n-s) [(2n-2s)!/(2n-2s)]/[(n-s)!/(n-s)]
                = (-1)^(n-s) (2n-2s)!/[2*(n-s)!]

請問哪裡錯？請指正，謝謝。

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