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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Power series for inverse Jacobian elliptic functions


Author: B. C. Carlson
Journal: Math. Comp. 77 (2008), 1615-1621
MSC (2000): Primary 33E05, 41A58, 33C45; Secondary 33C75
Published electronically: December 11, 2007
MathSciNet review: 2398783
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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$.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-07-02049-2
PII: S 0025-5718(07)02049-2
Keywords: Inverse Jacobian elliptic function, symmetric elliptic integral, Legendre polynomial
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