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Numerical calculation of elliptic integrals and elliptic functions. (English) Zbl 0133.08702

[1]Clenshaw, C. W., G. F. Miller, andM. Woodger: Handbook Series Special Functions, Algorithms for Special Functions I. Num. Math.4, 403-419 (1963). · Zbl 0107.11805 · doi:10.1007/BF01386339
[2]Bartky, W.: Numerical Calculation of a Generalized Complete Elliptic Integral. Rev. Mod. Phys.10, 264-269 (1938) · Zbl 0020.15604 · doi:10.1103/RevModPhys.10.264
[3]Alway, G. G.: Multhopp’s Influence Functions and their Automatic Computation. Quart. J. Mech.13, 112-118 (1960). · Zbl 0098.39502 · doi:10.1093/qjmam/13.1.112
[4]Hofsommer, D. J., andR. P. van de Riet: On the Numerical Calculation of Elliptic Integrals of the first and second kind and the Elliptic Functions of Jacobi. Num. Math.5, 291-302 (1963). · Zbl 0123.13204 · doi:10.1007/BF01385899
[5]Index by Subject to Algorithms, S 21. Communications of the ACM7, 146-148 (1964).
[6]Jahnke-Emde-Lösch: Tafeln höherer Funktionen, Tables of Higher Functions. Stuttgart: B. G. Teubner; New York: McGraw-Hill Book Comp., Inc. 1960.
[7]Byrd, P. F., andM. D. Friedman: Handbook of Elliptic Integrals for Engineers and Physicists. Berlin-Göttingen-Heidelberg: Springer 1954.
[8]Spenceley, G. W., andSpenceleyR. W.: Smithsonian Elliptic Functions Tables. Washington: Smithsonian Institution 1947.
[9]Legendre, A. M., u.F. Emde: Tafeln der elliptischen Normalintegrale erster und zweiter Gattung. Stuttgart: Wittwer 1931.
[10]Curtis, A. R.: N.P.L. Math. Tables, Vol. 7: Tables of Jacobian Elliptic Functions whose Arguments are Rational Fractions of the Quarter Period. London: Her Majesty’s Stationery Office 1964.
[11]Lee-Whiting, G. E.: Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind. J. of the A.C.M.10, 126-130 (1963).