On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function
Abstract
Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for [Formula: see text] due to Markov and rediscovered by Apéry. In this paper, we extend Koecher’s method to a very general setting and prove two more specific but still rather general results. As applications, we obtain infinite classes of identities for alternating Euler sums, further Markov–Apéry-type identities, and identities for even powers of [Formula: see text].