Evaluations of Derivatives of Jacobi Theta Functions in the origin

2011/05/28 by Nikos Bagis, Bagis, Nikos
Mathematics · #11M36 #14K25 #46G05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:11M36 #msc:14K25 #msc:46G05

paper · pdf · doi:10.48550/arxiv.1105.6279

9 pages

arxiv created 2011/05/28 · openalex publication_date 2011/05/28 · arxiv updated 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article using Ramanujan's theory of Eisenstein series we evaluate completely the derivatives of the theta functions ϑ₁^(2ν+1)(z) and ϑ₄^(2ν)(z) in the origin in closed polynomials forms using only the first three Eisenstein series of weights 2,4, and 6.

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