Winitzki. Uniform approximations of transcendental functions (LNCS)(10s).pdf: eKnigu

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Winitzki. Uniform approximations of transcendental functions (LNCS)(10s).pdf

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Date Oct 27, 2003

Our procedure is however more direct and easier to follow in hand calculations. 2.2 Global Approximations via Identities...
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Uniform Approximations for Transcendental Functions

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A heuristic approximation may be built using the approximate identity √ −x 2 4x πe 2 √ (erf x) + erf x ≈ 1 ⇒ erf x ≈ √ (22) −x 2 + 2x πe π e−2x2 + 16x2 (the author is grateful to Matthew Parry for bringing this to his attention)...
References
1. J. von zur Gathen and J. Gerhard, Modern Computer Algebra, Cambridge University Press, 1999. 2. M. Abramowitz and I. Stegun, Handbook of special functions, National Bureau of Standards, 1964. 3. P. Borwein, Canad. Math. Soc. Conf. Proc., 27 (2000), 29. 4. C. J. Lanczos, J. SIAM of Num. Anal. Ser. B, 1 (1964), 86; J. L. Sp ouge, J. SIAM of Num. Anal. 31 (1994), 931...