Representation of a class of multiple fractional part integrals and their closed form

Abstract

ABSTRACTIn this paper, the following generalized multiple fractional part integrals: and are considered for complex numbers , positive integers and positive number a, where denotes the fractional part of u. Furthermore, and can be transformed into the calculation of definite fractional part integral and , which overcomes the shortcomings of low speed and poor accuracy of the multiple case. Moreover, some identities and recursive formulas of the above integrals are obtained.