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Walker, Peter

The analyticity of Jacobian functions with respect to the parameter \(k\). (English) Zbl 1052.33018

Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 459, No. 2038, 2569-2574 (2003).
Summary: We show that the 12 Jacobian elliptic functions sn(\(z,k\)), etc., are meromorphic throughout the complex plane, as functions of \(k\) for fixed \(z\).

Cited in 10 Documents

MSC:

33E05 Elliptic functions and integrals

Keywords:

elliptic funcitons; Jacobian elliptic functions; meromorphic behaviour
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Digital Library of Mathematical Functions:

§22.17(ii) Complex Moduli ‣ §22.17 Moduli Outside the Interval [0,1] ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions
§22.2 Definitions ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions