MMN-748
Multiple fractional part integrals and Euler's constant
Abstract
The paper is about calculating multiple fractional part integrals of the form $\int_{0}^{1}\int_{0}^{1}(x+y)^{k}\left\{1/(x+y)\right\}^{p}dxdy$ and $\int_{0}^{1}\int_{0}^{1}\int_{0}^{1}\left\{1/(x+y+z)\right\}^{m}dxdydz$ where $\left\{x\right\}$ denotes the fractional part of $x$. We show that these integrals can be expressed as series involving products of Riemann zeta function values and some binomial coefficients. We obtain, as particular cases of our results, new integral representations of Euler's constant as double and triple symmetric fractional part integrals.
Vol. 17 (2016), No. 1, pp. 255-266
DOI: 10.18514/MMN.2016.748