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Computing elliptic integrals by duplication. (English) Zbl 0438.65029

65D20Computation of special functions, construction of tables
33E05Elliptic functions and integrals
30E20Integration, integrals of Cauchy type, etc. (one complex variable)
33B10Exponential and trigonometric functions
65D30Numerical integration
[1]Brent, R.P.: Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach.23, 242-251 (1976)
[2]Bulirsch, R.: Numerical calculation of elliptic integrals and elliptic functions. Numer. Math.7, 78-90, 353-354 (1965);13, 305-315 (1969) · Zbl 0133.08702 · doi:10.1007/BF01397975
[3]Carlson, B.C.: On computing elliptic integrals and functions. J. Math. and Phys.44, 36-51 (1965)
[4]Carlson, B.C.: Hidden symmetries of special functions. SIAM Rev.12, 332-345 (1970) · Zbl 0204.38503 · doi:10.1137/1012078
[5]Carlson, B.C.: An algorithm for computing logarithms and arctangents. Math. Comp.26, 543-549 (1972) · doi:10.1090/S0025-5718-1972-0307438-2
[6]Carlson, B.C.: Special Functions of Applied Mathematics. New York: Academic Press 1977
[7]Cazenave, R.: Intégrales et fonctions elliptiques en vue des applications. Centre de Documentation de l’Armement, Paris, 1969
[8]Fettis, H.E., Caslin, J.C.: Tables of elliptic integrals of the first, second and third kind. Report ARL 64-232, Wright-Patterson Air Force Base, Ohio, 1964. Errata in Math. Comp.20, 639-640 (1966) · doi:10.1090/S0025-5718-66-99913-3
[9]Franke, C.H.: Numerical evaluation of the elliptic integral of the third kind. Math. Comp.19, 494-496 (1965) · doi:10.1090/S0025-5718-1965-0178565-4
[10]Gautschi, W.: Computational methods in special functions ? a survey, (R. Askey, ed.) Theory and Application of Special Functions. New York: Academic Press 1975
[11]Heuman, C.: Tables of complete elliptic integrals. J. Math. and Phys.20, 127-206 (1941)
[12]Midy, P.: An improved calculation of the general elliptic integral of the second kind in the neighbourhood ofx=0. Numer. Math.25, 99-101 (1975) · Zbl 0312.65020 · doi:10.1007/BF01419531
[13]Milne-Thomson, L.M.: The Calculus of Finite Differences. London: Macmillan 1933
[14]Todd, J.: The lemniscate constants. Commun. ACM18, 14-19, 462 (1969) · Zbl 0298.33001 · doi:10.1145/360569.360580
[15]Van de Vel, H.: On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp.23, 61-69 (1969)
[16]Zill, D.G., Carlson, B.C.: Symmetric elliptic integrals of the third kind. Math. Comp.24, 199-214 (1970) · doi:10.1090/S0025-5718-1970-0262553-5