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

Sumit Kumar Jha

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arXiv · 2001.10533

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

Sumit Kumar Jha

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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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BibTeX RIS

Sumit Kumar Jha. 2020-01-28. On the Mellin transform of $\frac{\log^{n}(1+x)}{(1+x)^{m+1}}$. https://arxiv.org/abs/2001.10533

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