作者akrsw (quo vadis?)
看板Physics
标题Re: [物数] Factorial Function
时间Sun Feb 24 22:01:05 2008
※ 引述《Frobenius (▽．(▽×▽φ)=0)》之铭言：
: 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-s+1)...(2n-2s-1)
= (-1)^(n-s) (2n-2s-1)!/(n-s-1)!
= (-1)^(n-s) [(2n-2s)!/(2n-2s)]/[(n-s)!/(n-s)]
= (-1)^(n-s) (2n-2s)!/[2*(n-s)!]
请问哪里错？请指正，谢谢。
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 218.165.184.61
1F：推 Frobenius:想不到为什麽会多了1/2？ 02/24 23:11
2F：→ akrsw:对，我不知道为何会多出 1/2。 02/24 23:16
※ 编辑: akrsw 来自: 218.165.184.61 (02/24 23:22)