Inverse Error Function Table
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Inverse Erfc
JAVASCRIPT of the browser is OFF. Home/ Special Function/ Error function Inverse error function Calculator Calculates the inverse error function erf -1(y) and inverse complementary error function erfc -1(y). y0≦y≦1 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt Privacy Policy Terms of use FAQ Contact us © 2016 CASIO COMPUTER CO., LTD.
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Inverse Error Function Python
2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> inverse complementary error function Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram Language Commands> Inverse Erf The inverse erf function is the inverse error function c++ inverse function of the erf function such that (1) (2) with the first identity holding for and the second for . It is implemented in the Wolfram Language http://keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1180573448 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 (10) (which follows from the http://mathworld.wolfram.com/InverseErf.html 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 On-Line Encyclopedia of Integer Sequences." CITE THIS AS: Weisstein, Eric
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product Updates Documentation Home https://www.mathworks.com/help/symbolic/erfinv.html Symbolic Math Toolbox Examples Functions and Other Reference Release Notes PDF Documentation Mathematics Mathematical Functions Symbolic Math Toolbox Functions erfinv On this page Syntax Description Examples Inverse Error Function for Floating-Point and Symbolic Numbers Inverse Error Function for Complex Numbers Inverse Error Function for Variables and Expressions Inverse Error Function for Vectors and Matrices Special error function Values of Inverse Complementary Error Function Handling Expressions That Contain Inverse Complementary Error Function Plot Inverse Error Function Input Arguments X More About Inverse Error Function Tips Algorithms References See Also This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the inverse error function page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate erfinvInverse error functioncollapse all in page Syntaxerfinv(X) exampleDescriptionexampleerfinv(X
) computes the inverse error function of X. If X is a vector or a matrix, erfinv(X) computes the inverse error function of each element of X.ExamplesInverse Error Function for Floating-Point and Symbolic Numbers Depending on its arguments, erfinv can return floating-point or exact symbolic results. Compute the inverse error function for these numbers. Because these numbers are not symbolic objects, you