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The Ramanujan Journal

, Volume 34, Issue 3, pp 429–442 | Cite as

Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

  • Allal Ghanmi
  • Youssef Hantout
  • Ahmed Intissar
Article
  • 151 Downloads

Abstract

We provide two kinds of representations for the Taylor coefficients of the Weierstrass σ-function σ(⋅;Γ) associated to an arbitrary lattice Γ in the complex plane \(\mathbb{C}=\mathbb{R}^{2}\), the first one in terms of the so-called Hermite–Gauss series over Γ and the second one in terms of Hermite–Gauss integrals over \(\mathbb{C}\).

Keywords

Weierstrass sigma-function Taylor coefficients Poincaré series Theta functions Hermite–Gauss series 

Mathematics Subject Classification

33E05 42A16 13D40 11F27 14K25 

Notes

Acknowledgements

The authors are thankful to the anonymous referee and to the editor for their valuable suggestions for improving the presentation of the paper.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesMohammed V-Agdal UniversityRabatMorocco
  2. 2.UMR-CNRS 8524, UFR Math.USTLVilleneuve d’Ascq CedexFrance

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