Carlitz The Inverse Of The Error Function
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep inverse error function calculator 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and inverse complementary error function Analysis>Special Functions>Erf> Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram Language Commands> Inverse Erf The inverse erf function inverse error function python is the inverse function of the erf function such that (1) (2) with the first identity holding for and the second for . It is implemented in inverse error function c++ the Wolfram Language as InverseErf[x]. It is an odd function since (3) It has the special values (4) (5) (6) It is apparently not known if (7) (OEIS A069286) can be written in closed form. It satisfies the equation (8) where is the inverse erfc function. It has the derivative (9) and its integral is
Inverse Error Function Approximation
(10) (which follows from the method of Parker 1955). Definite integrals are given by (11) (12) (13) (14) (OEIS A087197 and A114864), where is the Euler-Mascheroni constant and is the natural logarithm of 2. The Maclaurin series of is given by (15) (OEIS A002067 and A007019). Written in simplified form so that the coefficient of is 1, (16) (OEIS A092676 and A092677). The th coefficient of this series can be computed as (17) where is given by the recurrence equation (18) with initial condition . SEE ALSO: Confidence Interval, Erf, Inverse Erfc, Probable Error RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/InverseErf/, http://functions.wolfram.com/GammaBetaErf/InverseErf2/ REFERENCES: Bergeron, F.; Labelle, G.; and Leroux, P. Ch.5 in Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, 1998. Carlitz, L. "The Inverse of the Error Function." Pacific J. Math. 13, 459-470, 1963. Parker, F.D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955. Sloane, N.J.A. Sequences A002067/M4458, A007019/M3126, A069286, A087197, A092676, A092677, A114859, A114860, and A114864 in "The O
Error Function §7.17 Inverse Error Functions Referenced by: §8.12 Permalink: http://dlmf.nist.gov/7.17 See also: info for 7 Contents §7.17(i) Notation §7.17(ii) Power Series §7.17(iii) Asymptotic Expansion
Inverse Error Function Excel
of inverfcx for Small x §7.17(i) Notation Keywords: error functions inverse error function wolfram alpha Permalink: http://dlmf.nist.gov/7.17.i See also: info for 7.17 The inverses of the functions x=erfy, x=erfcy, y∈ℝ, inverse error function c++ code are denoted by 7.17.1 y =inverfx, y =inverfcx, Defines: inverfcx: inverse complementary error function and inverfx: inverse error function Symbols: x: real variable Permalink: http://dlmf.nist.gov/7.17.E1 http://mathworld.wolfram.com/InverseErf.html Encodings: TeX, TeX, pMML, pMML, png, png See also: info for 7.17(i) respectively. §7.17(ii) Power Series Notes: See Carlitz (1963). Keywords: error functions Permalink: http://dlmf.nist.gov/7.17.ii See also: info for 7.17 With t=12πx, 7.17.2 inverfx=t+13t3+730t5+127630t7+⋯, |x|<1. Symbols: inverfx: inverse error function and x: real variable Permalink: http://dlmf.nist.gov/7.17.E2 Encodings: TeX, pMML, png See http://dlmf.nist.gov/7.17 also: info for 7.17(ii) For 25S values of the first 200 coefficients see Strecok (1968). §7.17(iii) Asymptotic Expansion of inverfcx for Small x Notes: (7.17.3) follows from Blair et al. (1976), after modifications. Keywords: error functions Permalink: http://dlmf.nist.gov/7.17.iii See also: info for 7.17 As x→0 7.17.3 inverfcx∼u-1/2+a2u3/2+a3u5/2+a4u7/2+⋯, Symbols: ∼: Poincaré asymptotic expansion, inverfcx: inverse complementary error function, x: real variable, ai: coefficients and u: expansion variable Referenced by: §7.17(iii) Permalink: http://dlmf.nist.gov/7.17.E3 Encodings: TeX, pMML, png See also: info for 7.17(iii) where 7.17.4 a2 =18v, a3 =-132(v2+6v-6), a4 =1384(4v3+27v2+108v-300), Defines: ai: coefficients (locally) Symbols: v: expansion variable Permalink: http://dlmf.nist.gov/7.17.E4 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png See also: info for 7.17(iii) 7.17.5 u=-2/ln(πx2ln(1/x)), Defines: u: expansion variable (locally) Symbols: lnz: principal branch of logarithm function and x: real variable Permalink: http://dlmf.nist.gov/7.17.E5 Encodings: TeX, pMML, png See also: info for 7.17(iii) and 7.17.6 v=ln(ln(1/x))-2+lnπ. Defines: v: expansion variable (locally) Symb
van GoogleInloggenVerborgen veldenBoekenbooks.google.nl - This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. https://books.google.com/books?id=hIPip3UxX3gC&pg=PA55&lpg=PA55&dq=carlitz+the+inverse+of+the+error+function&source=bl&ots=wdhfbQIFVC&sig=Wz7-5UBs6KArxJkHA2EecRKKt0s&hl=en&sa=X&ved=0ahUKEwiYkOnBj7nPAhVj74MKHQURBRgQ6AEIY The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution...https://books.google.nl/books/about/Computational_Methods_for_Physicists.html?hl=nl&id=hIPip3UxX3gC&utm_source=gb-gplus-shareComputational Methods for PhysicistsMijn bibliotheekHelpGeavanceerd zoeken naar boekeneBoek kopen - € 49,97Dit boek in gedrukte vorm bestellenSpringer ShopBol.comProxis.nlselexyz.nlVan StockumZoeken in een bibliotheekAlle verkopers»Computational Methods for Physicists: Compendium for StudentsSimon Sirca, error function Martin HorvatSpringer Science & Business Media, 17 dec. 2012 - 716 pagina's 0 Recensieshttps://books.google.nl/books/about/Computational_Methods_for_Physicists.html?hl=nl&id=hIPip3UxX3gCThis book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as inverse error function to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools. Voorbeeld weergeven » Wat mensen zeggen-Een recensie schrijvenWe hebben geen recensies gevonden op de gebruikelijke plaatsen.Geselecteerde pagina'sPagina 11InhoudsopgaveIndexInhoudsopgaveBasics of Numerical Analysis1 Solving Nonlinear Equations57 Matrix Methods109 Transformations of Functions and Signals159 Statistical Analysis and Modeling of Data207 Modeling and Analysis of Time Series277 Ini