Linear Arrangement of Euler Sums with Multiple Argument

Abstract

We investigate the linear arrangement of Euler harmonic sums that may be expressed in closed form in terms of special functions such as the classical Riemann zeta function and the Dirichlet eta function. Particular emphasis is given to Euler harmonic sums with even weight. New examples highlighting the theorems will be presented.

Keywords

• linear Euler sum
• polygamma function
• harmonic number
• polylogarithm function