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Analytic representations suitable for numerical computation of some special functions. (English) Zbl 0444.65002


MSC:

65B10 Numerical summation of series
33B15 Gamma, beta and polygamma functions
65D20 Computation of special functions and constants, construction of tables
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References:

[1] Abramowitz M, Stegun A (eds.) (1964) Handbook of mathematical functions. NBS Appl Math Ser No 55 · Zbl 0171.38503
[2] Estes R, Lancaster E (1972) Some generalized power series inversion. SIAM J Numer Anal 9:241-247 · Zbl 0239.65021 · doi:10.1137/0709023
[3] Rosser J (1951) Transformations to speed the convergence of series. J Res Nat Bur Standards Sect B46:56-64
[4] Takahasi H (1975) Complex function theory and numerical analysis (in Japanese). Kokyuroku of RIMS, Kyoto Univ No 253: 24-37
[5] Takahasi H (1980) Analytic continuation by variable transformation with application to summation of alternating series (in press)
[6] Takahasi H, Mori M (1973) Acceleration of convergence of Taylor series by variable transformation (in Japanese). Kokyuroku of RIMS, Kyoto Univ No 172:78-87
[7] Takahasi H, Mori M (1974) Double exponential formulas for numerical integration. Publ. RIMS. Kyoto Univ 9:721-741 · Zbl 0293.65011 · doi:10.2977/prims/1195192451
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