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arXiv · 1404.5143

A type of multiple integral with loggamma function

Duokui Yan·Rongchang Liu·Geng-zhe Chang
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Abstract

In this paper, we study the multiple integral $ \displaystyle I= \int_0^1 \int_0^1 \dots \int_0^1 f(x_1+x_2 + \dots +x_n) \, dx_1 \, dx_2 \, \dots \, dx_n$. A general formula of $I$ is presented. As an application, the integral $I$ with $f(x)= \log Γ(x)$ is evaluated. We show that the values of $I$ share a common formula for all $n \in \mathbb{N}$. The subsidiary computational challenges are substantial and interesting in their own right.

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Duokui Yan, Rongchang Liu, Geng-zhe Chang. 2014-04-21. A type of multiple integral with loggamma function. https://arxiv.org/abs/1404.5143

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