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Integral of product of irrational powers
Hello,
I'm trying to integrate a product of irrational "polynomials" that have arisen through dimensional regularization. As a warmup, I'm trying to understand how to integrate:
(w-a)^b (w-c)^d,
where b and d are arbitrary numbers, possibly irrational.
Mathematica can solve this indefinite integral, getting:
(((a - w)/(a - c))^-b (-a + w)^b (-c + w)^(1 + d)
Hypergeometric2F1[-b, 1 + d, 2 + d, (-c + w)/(a - c)])/(1 + d)
Can anyone explain how the answer is obtained?
Also, if there are any good tables (in print or online) or references on the subject of integrating
irrational powers, I would be very interested. Thank you.
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