http://www.johndcook.com/blog/2008/09/09/how-to-compute-binomial-coefficients/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 http://www.johndcook.com/blog/2008/09/09/how-to-compute-binomial-coefficients/comment-page-1/#comment-96569 I. J. Kennedy Thu, 04 Aug 2011 23:27:59 +0000 http://www.johndcook.com/blog/?p=382#comment-96569 Here's a nice <a href='http://mathoverflow.net/questions/20960/why-is-the-gamma-function-shifted-from-the-factorial-by-1' rel="nofollow">mathoverflow discussion</a> on the off-by-oneness of the gamma function. Here’s a nice mathoverflow discussion on the off-by-oneness of the gamma function.

]]> http://www.johndcook.com/blog/2008/09/09/how-to-compute-binomial-coefficients/comment-page-1/#comment-89409 John Fri, 24 Jun 2011 19:45:35 +0000 http://www.johndcook.com/blog/?p=382#comment-89409 Evan: There are historical reasons for the choice of definition of the gamma function. Gamma could have been defined so that for positive integers, Gamma(n) = n! instead of (n-1)!. Each choice of definition makes some formulas simpler and some more complicated. On balance, the standard definition simplifies more formulas than it complicates. At least that was the opinion of the people who standardized the definition, and I imagine a lot of people agree they made the right choice. Evan: There are historical reasons for the choice of definition of the gamma function. Gamma could have been defined so that for positive integers, Gamma(n) = n! instead of (n-1)!. Each choice of definition makes some formulas simpler and some more complicated. On balance, the standard definition simplifies more formulas than it complicates. At least that was the opinion of the people who standardized the definition, and I imagine a lot of people agree they made the right choice.

]]> http://www.johndcook.com/blog/2008/09/09/how-to-compute-binomial-coefficients/comment-page-1/#comment-89401 Evan Fri, 24 Jun 2011 18:52:35 +0000 http://www.johndcook.com/blog/?p=382#comment-89401 can someone explain to me why the use gamma of z or w plus one? Why can'tthey just do z! or w!? that would be so much easier, right? can someone explain to me why the use gamma of z or w plus one? Why can’tthey just do z! or w!? that would be so much easier, right?

]]> http://www.johndcook.com/blog/2008/09/09/how-to-compute-binomial-coefficients/comment-page-1/#comment-6360 John Venier Tue, 09 Sep 2008 16:30:00 +0000 http://www.johndcook.com/blog/?p=382#comment-6360 An interesting exercise is to calculate the exact number of trailing zeros in (n!) for large (n), such as (99!) or (1000!). An interesting exercise is to calculate the exact number of trailing zeros in (n!) for large (n), such as (99!) or (1000!).

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