Further results on generalized multiple fractional part integrals for complex values

摘要

In this paper, the following multiple fractional part integrals and are studied for positive integer and complex values of , where denotes the fractional part of , denotes the real part of and . It is proved that can be represented as a linear combination of the Riemann zeta function, the Beta function and Euler’s constant as . Moreover, can be expressed by , the Beta function and the incomplete Beta function for . In addition, the recurrence formula of is established and can be expressed by , logarithmic function and some binomial coefficients.