Domain of the regularized incomplete beta function?

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sgfw
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Joined: Wed Jun 19, 2013 11:47 pm UTC

Domain of the regularized incomplete beta function?

Postby sgfw » Sun Jun 29, 2014 4:40 pm UTC

I've been making an algorithm for the regularized incomplete beta function, which pretty much just uses the continued fraction given here, along with the property that Ix(a, b) = I1-x(b, a), which works, mostly. The algorithm has an error when a or b are negative integers, which makes sense because the gamma function, which is evaluated at both a and b in the definition, is undefined at negative integers. The thing is, wolfram|alpha has no problem with it. There are a few more examples of this, but what I would really like is an explicit domain of the regularized incomplete beta function, for imaginary arguments as well as real ones. Can anyone help with this?

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