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Computing elliptic integrals by duplication. (English) Zbl 0438.65029

65D20 Computation of special functions and constants, construction of tables
33E05 Elliptic functions and integrals
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
33B10 Exponential and trigonometric functions
65D30 Numerical integration
Full Text: DOI EuDML
[1] Brent, R.P.: Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach.23, 242-251 (1976) · Zbl 0324.65018
[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) · Zbl 0163.39601
[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) · Zbl 0244.65011 · doi:10.1090/S0025-5718-1972-0307438-2
[6] Carlson, B.C.: Special Functions of Applied Mathematics. New York: Academic Press 1977 · Zbl 0394.33001
[7] Cazenave, R.: IntĂ©grales 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) · Zbl 0156.17304 · 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 · Zbl 0325.33001
[11] Heuman, C.: Tables of complete elliptic integrals. J. Math. and Phys.20, 127-206 (1941) · Zbl 0025.06703
[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 · JFM 59.1111.01
[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) · Zbl 0187.10201
[16] Zill, D.G., Carlson, B.C.: Symmetric elliptic integrals of the third kind. Math. Comp.24, 199-214 (1970) · Zbl 0199.50001 · doi:10.1090/S0025-5718-1970-0262553-5
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