Infinite Series Concerning Tails of Riemann Zeta Values

Abstract

Infinite series involving Riemann’s zeta and Dirichlet’s lambda tails, and weighted by three harmonic-like elementary symmetric functions are examined. By means of integral representations of zeta tails together with the telescopic approach, twelve general summation theorems are established that express these series as coefficients of the bivariate beta function Beta(u,v). By further expanding Beta(u,v) into Laurent series in u and v, several explicit summation formulae are shown as consequences.

Keywords

• Riemann zeta function
• Dirichlet lambda function
• gamma function
• beta function