Beta function integral representation

Beta function integral representation

[@AbhaySingh-uz3zl]

This is some strange coincidence. Today , in our final paper of Integral Transforms, this question came. I think even our professor watches your videos

[@khiemngo1098]

Thanks for sharing! I understand your proof but what I don't understand is where you got your version of the Beta function which doesn't look like anything I have seen. The Beta function, by definition, is the integral defined from 0 to 1 but yours goes from 0 to infinity. In addition, the integrand doesn't look familiar. Can you please point me to a resource where you got the formula B(a, b) = int_0^infinity x^(a - 1)/(1 + x)^(a + b) ? Many thanks!