Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function $\textrm {sn}(x, k)$
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- by Staffan Wrigge PDF
- Math. Comp. 36 (1981), 555-564 Request permission
Abstract:
The Taylor series expansion coefficients of the Jacobian elliptic function ${\text {sn}}(x,k)$ and its power ${\text {sn}}^2(x,k)$ are studied. Recurrence formulae are given, and tables of the coefficients constructed. Using Lagrange’s inversion formula, these coefficients can be expressed in terms of Legendre polynomials.References
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M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, Nat. Bur. Standards, Appl. Math. Series No. 55, December 1972.
- F. Bowman, Introduction to elliptic functions with applications, Dover Publications, Inc., New York, 1961. MR 0132214
- Dominique Dumont, A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions, Math. Comp. 33 (1979), no. 148, 1293–1297. MR 537974, DOI 10.1090/S0025-5718-1979-0537974-1 H. Hancock, Lectures on the Theory of Elliptic Functions, Dover, New York, 1958. I. S. Gradshteyn & I. M. Ryshik, Tables of Series, Products and Integrals, Academic Press, New York, 1965.
- Alois Schett, Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions, Math. Comp. 30 (1976), no. 133, 143–147. MR 391477, DOI 10.1090/S0025-5718-1976-0391477-3 E. T. Whittaker & G. N. Watson, Modern Analysis, Cambridge Univ. Press, Cambridge, 1927.
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 555-564
- MSC: Primary 65D20; Secondary 33A25
- DOI: https://doi.org/10.1090/S0025-5718-1981-0606513-8
- MathSciNet review: 606513