Evaluations of Derivatives of Jacobi Theta Functions in the origin

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.

9 pages

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