A note on the Taylor series expansion coefficients of the Jacobian elliptic function
Author:
Staffan Wrigge
Journal:
Math. Comp. 37 (1981), 495497
MSC:
Primary 33A25
MathSciNet review:
628709
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Abstract: By considering and as power series in the modulus k, closed expressions are obtained for some of the integers occurring in the polynomials considered.
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 F. Bowman, Introduction to Elliptic Functions with Applications, Dover, New York, 1961. MR 0132214 (24:A2060)
 [2]
 D. Dumont, "A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions," Math. Comp., v. 33, 1979, pp. 12931297. MR 537974 (80i:33003)
 [3]
 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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 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, New York, 1962. MR 0178117 (31:2375)
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 S. Wrigge, "Calculation of the Taylor series expansion coefficients of the Jacobian ellipticfunction ," Math. Comp., v. 36, 1981, pp. 555564. MR 606513 (82d:65023)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106287091
PII:
S 00255718(1981)06287091
Keywords:
Elliptic functions,
Laplace transforms
Article copyright:
© Copyright 1981
American Mathematical Society
