Short List of Jacobi Elliptic Functions and Constants Used in Chap. 5

Dittrich, Walter

doi:10.1007/978-3-030-69105-9_6

Walter Dittrich¹⁷

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

The Jacobi elliptic functions sn(z, k), cn(z, k) and dn(z, k) can be represented by means of elliptic integrals, e.g.,

$$\begin{aligned} z = \int \limits ^{sn (z, k)}_0 \frac{1}{\sqrt{(1 - t^2) (1 - k^2 t^2)}} dt \, . \end{aligned}$$

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Institute of Theoretical Physics, University of Tübingen, Tübingen, Baden-Württemberg, Germany
Walter Dittrich

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Dittrich, W. (2021). Short List of Jacobi Elliptic Functions and Constants Used in Chap. 5. In: The Development of the Action Principle . SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-69105-9_6

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DOI: https://doi.org/10.1007/978-3-030-69105-9_6
Published: 30 May 2021
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-69104-2
Online ISBN: 978-3-030-69105-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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Short List of Jacobi Elliptic Functions and Constants Used in Chap. 5