Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593591 | Journal of Number Theory | 2015 | 22 Pages |
Abstract
In this article, we present a variety of evaluations of series of polylogarithmic nature. More precisely, we express the special values at positive integers of two classes of zeta functions of Arakawa–Kaneko-type by means of certain inverse binomial series involving harmonic sums which appeared fifteen years ago in physics in relation to the Feynman diagrams. In some cases, these series may be explicitly evaluated in terms of zeta values and other related numbers. Incidentally, this connection allows us to deduce new identities for the constant C=∑n≥11(2n)3(1+13+⋯+12n−1) considered by S. Ramanujan in his notebooks.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marc-Antoine Coppo, Bernard Candelpergher,