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An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind. (English) Zbl 0175.46001
[1]Abramowitz, M., andI. A. Stegun: Handbook of mathematical functions. New York: Dover (1965)
[2]Alway, G. G.: Multhopp’s influence functions and their automatic computation. Quart. J. Mech.13, 192–918 (1960). · Zbl 0098.39502 · doi:10.1093/qjmam/13.1.112
[3]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
[4]Bulirsch, R.: Numerical calculation of elliptic integrals and elliptic functions I, II. Numer. Math.7, 78–90, 353–354 (1965). · Zbl 0133.08702 · doi:10.1007/BF01397975
[5]—-, u.J. Stoer: Darstellung von Funktionen in Rechenautomaten. Contrib. to ”Mathematische Hilfsmittel des Ingenieurs III”, Editors:R. Sauer, I. Szábo. Berlin-Heidelberg-New York: Springer 1968.
[6]– Numerical calculation of elliptic integrals and elliptic functions III. To appear in Numer. Math.
[7]Byrd, P. F., andM. D. Friedman: Handbook of elliptic integrals for engineers and physicists. Berlin-Göttingen-Heidelberg: Springer 1954.
[8]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 Stationary Office 1964.
[9]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
[10]Jahnke-Emde-Lösch: Tafeln höherer Funktionen; Tables of higher functions. Stuttgart: Teubner; New York: McGraw-Hill 1960.
[11]King, A. V.: On the direct numerical calculation of elliptic functions and integrals. London: Cambr. Un. Press 1924.
[12]Tölke, F.: Praktische Funktionenlehre II, III. Berlin-Heidelberg-New York: Springer 1966.
[13]Fettis, H. E.: Calculation of elliptic integrals of the third kind by means of Gauss’ transformation. Math. Comp.19, 97–104 (1965).