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- W3132154328 abstract "We study the function series $sum_{n=1}^infty phi^{2m+2} text{cosch}^{2m+2}(nphi/2)$, 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 $phi=pm 2pi i$. We furthermore derive several identities between Harmonic numbers and ordinary and generalized Bernoulli polynomials." @default.
- W3132154328 created "2021-03-01" @default.
- W3132154328 creator A5087701571 @default.
- W3132154328 date "2021-02-17" @default.
- W3132154328 modified "2023-09-27" @default.
- W3132154328 title "Functional relations for hyperbolic cosecant series" @default.
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