Evaluations of Derivatives of Jacobi Theta Functions in the origin

Nikos Bagis

Evaluations of Derivatives of Jacobi Theta Functions in the origin

General Mathematics 2011-06-01 v1

Authors: Nikos Bagis

Abstract

In this article using Ramanujan's theory of Eisenstein series we evaluate completely the derivatives of the theta functions $\vartheta_1^{(2\nu+1)}(z)$ and $\vartheta_4^{(2\nu)}(z)$ in the origin in closed polynomials forms using only the first three Eisenstein series of weights 2,4, and 6.

Keywords

Jacobi theta functions derivatives at origin Eisenstein series Ramanujan's theory closed polynomial forms

Cite

@article{arxiv.1105.6279,
  title  = {Evaluations of Derivatives of Jacobi Theta Functions in the origin},
  author = {Nikos Bagis},
  journal= {arXiv preprint arXiv:1105.6279},
  year   = {2011}
}

Comments

9 pages

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