Generalization of the non-local derangement identity and applications to multiple zeta-type series

Abstract

The goal of this paper is the study of a transformation concerning the general K-fold finite sums of the form

Sigma (N >= n1 >= ... >= nK >= 1) 1/b(nK) . Pi (K-1)(J=1) 1/a(nj),

where (K,N) is an element of N-2 and {a(n)}(n=1)(infinity), {b(n)}(n=1)(infinity) are appropriate real sequences. In the application part of our paper we apply the developed transformation to two special parametric multiple zeta-type series that generalize the well-know formula zeta(star)({2}(K), 1) = 2 zeta(2K + 1), K is an element of N. As a corollary of our parametric results, we also prove several sum formulas involving multiple zeta-star values.