Error Function Inverse
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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 error function inverse calculator entries Last updated: Tue Sep 27 2016 Created, developed, error function values and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram inverse complementary error function Language Commands> Inverse Erf The inverse erf function is the inverse function of the erf function such that (1) (2) with the first identity holding inverse erfc function for and the second for . It is implemented in 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)
Inverse Erfc
where is the inverse erfc function. It has the derivative (9) and its integral is (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. 1
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
Inverse Error Function Excel
Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and inverse error function matlab Analysis>Special Functions>Erf> Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram Language Commands> Inverse Erfc The inverse erf inverse error function table function is the inverse function of such that (1) with the first identity holding for and the second for . It is implemented in the Wolfram Language http://mathworld.wolfram.com/InverseErf.html as InverseErfc[z]. It is related to inverse erf by (2) It has the special values (3) (4) (5) It has the derivative (6) and its indefinite integral is (7) (which follows from the method of Parker 1955). The Taylor series about 1 is given by (8) (OEIS A002067 and A007019). SEE ALSO: Erfc, Inverse Erf http://mathworld.wolfram.com/InverseErfc.html RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/InverseErfc/ 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, A092676, and A092677 in "The On-Line Encyclopedia of Integer Sequences." CITE THIS AS: Weisstein, Eric W. "Inverse Erfc." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseErfc.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Wolfram Problem Generator»
Error Function Free Statistics Calculators: Home > Inverse Error error function Function Calculator Inverse Error Function Calculator This calculator will compute the value of the inverse error function, given the limit of inverse error function integration x. The inverse error function is also known as the Gauss inverse error function.Please enter the necessary parameter values, and then click 'Calculate'. x: Related Resources Calculator Formulas References Related Calculators Search Free Statistics Calculators version 4.0 The Free Statistics Calculators index now contains 106 free statistics calculators! Copyright © 2006 - 2016 by Dr. Daniel Soper. All rights reserved.
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