Identities in the spirit of Euler

Abstract

In this paper we develop new identities in the spirit of Euler. We shall investigate and report on new Euler identities of weight p + 2, for p an odd integer, but with a non unitary argument of the harmonic numbers. Some examples of these Euler identities will be given in terms of Riemann zeta values, Dirichlet values and other special functions.

Keywords

• Polylogarithm function
• recurrence relations
• Euler sums
• Zeta functions
• Dirichlet functions
• Multiple zeta values