Abstract
Letτbe a complex number, with Im τ>0. Letω1be defined as a function ofτby the relation
and let\( {\omega _{2}} = {\omega _{1}} \cdot \tau \). The Jacobian elliptic function snuis a doubly-periodic, meromorphic function ofu, with\( \left( {{\omega _{1}},{\omega _{2}}} \right) \)as a pair of basic periods, with two simple poles in each period-parallelogram, the sum of the residues at those poles being zero. It satisfies the differential equation
, where
.
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© 1985 Springer-Verlag Berlin Heidelberg
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Chandrasekharan, K. (1985). The Jacobian elliptic functions and the modular functionλ(τ). In: Elliptic Functions. Grundlehren der mathematischen Wissenschaften, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52244-4_7
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DOI: https://doi.org/10.1007/978-3-642-52244-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-52246-8
Online ISBN: 978-3-642-52244-4
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