Elliptic functions to the quintic base

• Autores: Heng Huat Chan, Zhi-Guo Liu
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 226, Nº 1, 2006, págs. 53-64
• Idioma: inglés
• DOI: 10.2140/pjm.2006.226.53
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• Resumen

  • We study two elliptic functions to the quintic base and find two nonlinear second order differential equations satisfied by them. We then derive two recurrence relations involving certain Eisenstein series associated with the group G0(5). These recurrence relations allow us to derive infinite families of identities involving the Eisenstein series and Dedekind ?-products. An imaginary transformation for one of the elliptic functions is also derived.