On the Mellin transform of $\frac{{\log }^n(1+x)}{(1+x{)}^{m+1}}$

Abstract

We use the Ramanujan's master theorem to evaluate the integral $${\int }_0^{\infty }\frac{x^{l-1}}{(1+x{)}^{m+1}}{\log }^n(1+x)dx$$ in terms of the digamma function, the gamma function, and the Hurwitz zeta function.

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