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Computing elliptic integrals by duplication. (English) Zbl 0438.65029

MSC:
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
References:
[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