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

Some series whose coefficients involve the valueζ(n)for $n$nodd