Identity families of multiple harmonic sums and multiple zeta star values

Central Binomial Sums, Multiple Clausen Values, and Zeta Values

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ra...

On Mordell-tornheim Sums and Multiple Zeta Values

RÉSUMÉ. Nous prouvons que toute somme de Mordell-Tornheim avec des arguments entiers positifs peut s’écrire comme une combinaison linéaire rationnelle de valeurs prises par des fonctions multi-zêta ayant le même poids et la même profondeur. Selon un résultat de Tsumura, il s’ensuit que toute somme de Mordell-Tornheim ayant un poids et une profondeur de parité différente peut s’exprimer comme un...

On some explicit evaluations of multiple zeta-star values

In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of π. 1 Main Results The multiple zeta value (MZV) is defined by the convergent series ζ(k1, k2, . . . , kn) := ∑ m1>m2>···>mn>0 1 m1 1 m k2 2 · · ·m kn n , where k1, k2, . . . , kn are positive integers and k1 ≥ 2. The integers k = k1+k2+ · · ·+kn and n are called weight and dept...

A Combinatorial Identity of Multiple Zeta Values with Even Arguments

Let ζ(s1, s2, · · · , sk;α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k 6 n, let E(2n, k;α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k;α).

New Families of Weighted Sum Formulas for Multiple Zeta Values