Abstract
In this paper, the following multiple fractional part integrals
and
are calculated for non-negative integers
and positive integer n, where
denotes the fractional part of u and
It is proved that
has a closed form for non-negative integer
. We also prove that
(
and
) and
can be expressed as linear combinations of the Riemann zeta function, logarithmic function and some binomial coefficients. In particular,
has a closed form for
. Moreover, some identities and recursive formulas of the above integrals are obtained.
Disclosure statement
No potential conflict of interest was reported by the authors.