  We study the function series $\sum_{n=1}^\infty \phi^{2m+2}
\text{cosch}^{2m+2}(n\phi/2)$, and similar series, for integers $m$ and complex
$\phi$. This hyperbolic series is linearly related to the Lambert series. The
Lambert series is known to satisfy a functional equation which defines the
Ramanujan polynomials. By using residue theorem (summation theorem) we find the
functional equation satisfied by this hyperbolic series. The functional
equation identifies a class of polynomials which can be seen as a
generalization of the Ramanujan polynomials. These polynomials coincide with
the asymptotic expansion of the hyperbolic series at the origin and they all
vanish for $\phi=\pm 2\pi i$. We furthermore derive several identities between
Harmonic numbers and ordinary and generalized Bernoulli polynomials.
