Fourier series coefficients for powers of the Jacobian elliptic functions
Author:
AyΕe Kiper
Journal:
Math. Comp. 43 (1984), 247259
MSC:
Primary 33A25
MathSciNet review:
744934
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Abstract: The Fourier series expansion coefficients for the Jacobian elliptic functions , and , with , are studied. Twoterm recurrence formulae are obtained and some of the coefficients are tabulated.
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 [2]
 P. F. Byrd & M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, 2nd ed., SpringerVerlag, Berlin, 1971. MR 0277773 (43:3506)
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 P. Du Val, Elliptic Functions and Elliptic Curves, London Mathematical Society Lecture Note Series 9, Cambridge Univ. Press, Cambridge, 1973. MR 0379512 (52:417)
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 A. Fransén, "Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function ," Math. Comp., v. 37, 1981, pp. 475494. MR 628708 (83a:33003)
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 R. G. Langebartel, "Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions," SIAM J. Math. Anal., v. 11, 1980, pp. 506513. MR 572201 (81e:42008)
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 A. Schett, "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions," Math. Comp., v. 30, 1976, pp. 143147. MR 0391477 (52:12298)
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 A. Schett, Addendum to "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions," Math. Comp., v. 31, 1977, Microfiche supplement.
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 A. Schett, "Recurrence formula of the Taylor series expansion coefficients of the Jacobian elliptic functions," Math. Comp., v. 31, 1977, pp. 10031005. MR 0442301 (56:687)
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 E. T. Whittaker & G. N. Watson, Modern Analysis, Cambridge Univ. Press, Cambridge, 1962. MR 0178117 (31:2375)
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 S. Wrigge, "Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function ," Math. Comp., v. 36, 1981, pp. 555564. MR 606513 (82d:65023)
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 S. Wrigge, "A note on the Taylor series expansion coefficients of the Jacobian elliptic function ," Math. Comp., v. 37, 1981, pp. 495497. MR 628709 (83a:33004)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407449346
PII:
S 00255718(1984)07449346
Article copyright:
© Copyright 1984
American Mathematical Society
