A type of multiple integral with log-gamma function
Copyright policy )A type of multiple integral with log-gamma function
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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- University of Science and Technology of China China (People's Republic of)
- Beihua University China (People's Republic of)
- Beihang University China (People's Republic of)
05A19, multiple integral, Mathematics - Classical Analysis and ODEs, log-gamma function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 54C30
05A19, multiple integral, Mathematics - Classical Analysis and ODEs, log-gamma function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 54C30
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