Power series for inverse Jacobian elliptic functions
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- by B. C. Carlson PDF
- Math. Comp. 77 (2008), 1615-1621 Request permission
Abstract:
The 12 inverse Jacobian elliptic functions are expanded in power series by using properties of the symmetric elliptic integral of the first kind. Suitable notation allows three series to include all 12 cases, three of which have been given previously. All coefficients are polynomials in the modulus $k$ that are homogeneous variants of Legendre polynomials. The four series in each of three subsets have the same coefficients in terms of $k$.References
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Additional Information
- B. C. Carlson
- Affiliation: Ames Laboratory and Department of Mathematics, Iowa State University, Ames, Iowa 50011-3020
- Email: bcarlson@scl.ameslab.gov
- Received by editor(s): September 6, 2006
- Received by editor(s) in revised form: March 1, 2007
- Published electronically: December 11, 2007
- Additional Notes: Work at the Ames Laboratory was supported by the Department of Energy-Basic Energy Sciences under Contract No. DE-AC02-07CH11358
- Journal: Math. Comp. 77 (2008), 1615-1621
- MSC (2000): Primary 33E05, 41A58, 33C45; Secondary 33C75
- DOI: https://doi.org/10.1090/S0025-5718-07-02049-2
- MathSciNet review: 2398783