Some series whose coefficients involve the value ζ(n) for $n$n odd

Abstract

By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values (2n+1), n=1,2,⋯, of the Riemann-zeta function. A number of these have a combinatorial flavor which we also express in a trignometric form for special choices of the underlying variable. We briefly touch upon their use in the representation of solutions of the wave equation.