Chapter 22Jacobian Elliptic Functions
W. P. ReinhardtUniversity of Washington, Seattle, Washington.P. L. WalkerAmerican University of Sharjah, Sharjah, United Arab Emirates.
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- Acknowledgements:
- This chapter is based in part onAbramowitz and Stegun (1964, Chapters 16,18) by L. M. Milne-Thomson andT. H. Southard respectively.
- Notes:
- The references used for the mathematical properties in this chapter areArmitage and Eberlein (2006),Bowman (1953),Copson (1935),Lawden (1989),McKean and Moll (1999),Walker (1996),Whittaker and Watson (1927),and for physical applicationsDrazin and Johnson (1993),Lawden (1989),Walker (1996).The references used for the mathematical properties in this chapter areArmitage and Eberlein (2006),Bowman (1953),Copson (1935),Lawden (1989),McKean and Moll (1999),Walker (1996),Whittaker and Watson (1927),and for physical applicationsDrazin and Johnson (1993),Lawden (1989),Walker (1996).
- Referenced by:
- §32.2(i),New Associate Editors for the DLMF,ProfileHans Volkmer,ProfilePeter L. Walker,ProfileWilliam P. Reinhardt,ProfileWilliam P. Reinhardt,§ ‣Chapter Authors,§ ‣Chapter Authors,§ ‣Associate Editors,§ ‣Associate Editors,§ ‣Associate Editors,Erratum (V1.0.1) for References,§ ‣Software Cross Index
- Permalink:
- http://dlmf.nist.gov/22
- Addition (effective with 1.0.1):
- Armitage and Eberlein (2006) was added as a general reference for this chapter.
- Notation
- Properties
- 22.2Definitions
- 22.3Graphics
- 22.4Periods, Poles, and Zeros
- 22.5Special Values
- 22.6Elementary Identities
- 22.7Landen Transformations
- 22.8Addition Theorems
- 22.9Cyclic Identities
- 22.10Maclaurin Series
- 22.11Fourier and Hyperbolic Series
- 22.12Expansions in Other Trigonometric Series and Doubly-Infinite PartialFractions: Eisenstein Series
- 22.13Derivatives and Differential Equations
- 22.14Integrals
- 22.15Inverse Functions
- 22.16Related Functions
- 22.17Moduli Outside the Interval [0,1]
