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The Distribution of the Zeros of Jacobian Elliptic Functions with Respect to the Parameter k

The Distribution of the Zeros of Jacobian Elliptic Functions with Respect to the Parameter k We investigate the distribution of the zeros of the twelve Jacobian elliptic functions sn(z, k), etc. as functions of k for fixed z. We show that the number of zeros inside a disc given by ¦k¦ ≤ r is approximately of order r 2 and hence that the mapping k ↦ sn(z, k) is of order 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

The Distribution of the Zeros of Jacobian Elliptic Functions with Respect to the Parameter k

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321746
Publisher site
See Article on Publisher Site

Abstract

We investigate the distribution of the zeros of the twelve Jacobian elliptic functions sn(z, k), etc. as functions of k for fixed z. We show that the number of zeros inside a disc given by ¦k¦ ≤ r is approximately of order r 2 and hence that the mapping k ↦ sn(z, k) is of order 2.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 23, 2009

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