Mathematics of Computation

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6842(e) ISSN 0025-5718(p)

Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function ${\rm sn}(x,\,k)$

Author(s): Staffan Wrigge.
Journal: Math. Comp. 36 (1981), 555-564.
MSC: Primary 65D20; Secondary 33A25
MathSciNet review: 606513
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[1]: 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.
[2]: F. Bowman, Introduction to Elliptic Functions with Applications, Dover, New York, 1961. MR 0132214 (24:A2060)
[3]: D. Dumont, "A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions," Math. Comp., v 33, 1979, pp. 1293-1297. MR 537974 (80i:33003)
[4]: H. Hancock, Lectures on the Theory of Elliptic Functions, Dover, New York, 1958.
[5]: I. S. Gradshteyn & I. M. Ryshik, Tables of Series, Products and Integrals, Academic Press, New York, 1965.
[6]: A. Schett, "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions," Math. Comp., v. 30, 1976, pp. 143-147. MR 0391477 (52:12298)
[7]: E. T. Whittaker & G. N. Watson, Modern Analysis, Cambridge Univ. Press, Cambridge, 1927.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|