How to compute binomial coefficients

My previous post showed how to define binomial coefficients for general arguments.¬† I just posted¬†an article that explains how to compute binomial coefficients. Here’s a chart from the article for computing the binomial coefficient (z, w) for arbitrary complex z and w.

See also How to calculate binomial probabilities.

Posted in Math
4 comments on “How to compute binomial coefficients
  1. John Venier says:

    An interesting exercise is to calculate the exact number of trailing zeros in (n!) for large (n), such as (99!) or (1000!).

  2. Evan says:

    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?

  3. John says:

    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.

  4. I. J. Kennedy says:

    Here’s a nice mathoverflow discussion on the off-by-oneness of the gamma function.