Dear friends,

while working with Beta function integrals like int_0^1 x^(7/23)*(1-x)^(16/23) dx I noticed that Maple does not seem to know about the following Beta function identity:

Beta(m+q, n+1-q) = Pi/sin(Pi*q)*mul(r+q, r=0..m-1)*mul(r+1-q, r=0..n-1)/(m+n)!

where m,n are positive integers and q is a real number so that 0 < q < 1. This is easy to prove and there is a whole family of identities of this type, obtainable whenever the two Beta function arguments add up to an integer.

This seems like a useful identity to have. Or maybe it is built in already and only needs to be deployed properly. In any case it would help produce more useful answers for integrals like the one above.

Best regards,

Marko Riedel


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