Euler sums and integrals of polylogarithm functions
نویسندگان
چکیده
منابع مشابه
Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
We show that integrals of the form ∫ 1 0 xLip(x)Liq(x)dx (m ≥ −2, p, q ≥ 1) and ∫ 1 0 log(x)Lip(x)Liq(x) x dx (p, q, r ≥ 1) satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, in the first case for all m, p, q and in the second case when p+ q+ r is even, these integrals are reducible to zeta values. In the case of odd p+q+r, we comb...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.01.025