Evaluate Error Function In Mathematica
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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 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> Calculus and Analysis>Complex Analysis>Entire Functions> Interactive
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Entries>webMathematica Examples> More... History and Terminology>Wolfram Language Commands> MathWorld Contributors>D'Orsogna> Less... Erf is the "error mathematica erfc function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined
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by (1) Note that some authors (e.g., Whittaker and Watson 1990, p.341) define without the leading factor of . Erf is implemented in the Wolfram Language as Erf[z]. A two-argument form giving is also implemented as Erf[z0, https://reference.wolfram.com/language/ref/Erf.html z1]. Erf satisfies the identities (2) (3) (4) where is erfc, the complementary error function, and is a confluent hypergeometric function of the first kind. For , (5) where is the incomplete gamma function. Erf can also be defined as a Maclaurin series (6) (7) (OEIS A007680). Similarly, (8) (OEIS A103979 and A103980). For , may be computed from (9) (10) (OEIS A000079 and A001147; Acton 1990). For , (11) (12) Using integration http://mathworld.wolfram.com/Erf.html by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). Erf has the values (21) (22) It is an odd function (23) and satisfies (24) Erf may be expressed in terms of a confluent hypergeometric function of the first kind as (25) (26) Its derivative is (27) where is a Hermite polynomial. The first derivative is (28) and the integral is (29) Min Max Re Im Erf can also be extended to the complex plane, as illustrated above. A simple integral involving erf that Wolfram Language cannot do is given by (30) (M.R.D'Orsogna, pers. comm., May 9, 2004). More complicated integrals include (31) (M.R.D'Orsogna, pers. comm., Dec.15, 2005). Erf has the continued fraction (32) (33) (Wall 1948, p.357), first stated by Laplace in 1805 and Legendre in 1826 (Olds 1963, p.139), proved by Jacobi, and rediscovered by Ramanujan (Watson 1928; Hardy 1999, pp.8-9). Definite integrals involving include Definite integrals involving include (34) (35) (36) (37) (38) The first two of these appear in Prudnikov et al. (1990, p.123, eqns. 2.8.19.8 and 2.8.19.11), with , . A complex generalization of is defined as (39) (40) Integral representations valid only in the upper half-plane are given by (41) (42) SEE ALSO: Dawson's Integral, Erfc, Erfi, Fresnel I
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 http://mathworld.wolfram.com/Erfi.html Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> Calculus and Analysis>Complex Analysis>Entire Functions> Interactive Entries>webMathematica Examples> History and Terminology>Wolfram Language Commands> Erfi http://mathematica.stackexchange.com/questions/40005/evaluate-in-plot-leads-to-function-error Min Max Min Max Re Im The "imaginary error function" is an entire function defined by (1) where is the erf function. It is implemented in the error function Wolfram Language as Erfi[z]. has derivative (2) and integral (3) It has series about given by (4) (where the terms are OEIS A084253), and series about infinity given by (5) (OEIS A001147 and A000079). SEE ALSO: Dawson's Integral, Erf, Erfc RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/Erfi/ REFERENCES: Sloane, N.J.A. Sequences A000079/M1129, A001147/M3002, and A084253 in "The evaluate error function On-Line Encyclopedia of Integer Sequences." Referenced on Wolfram|Alpha: Erfi CITE THIS AS: Weisstein, Eric W. "Erfi." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Erfi.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» Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Language» Knowledge-based programming for everyone. Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc.
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematica Questions Tags Users Badges Unanswered Ask Question _ Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Evaluate in Plot leads to function error up vote 3 down vote favorite 1 Please help - I'm really struggling to understand why this evaluates with errors. data = RandomReal[10, {4, 1000}]; metric[data_, perc_] := (x = Quantile[#, perc] & /@ data; Accumulate[x]/Total[x]); Plot[Evaluate@metric[data, p], {p, 0.01, 0.99}, AxesLabel -> {"Percentile", "Proportion"}, PlotLegends -> {"Series A", "Series A+B", "Series A+B+C", "Series A+B+C+D"}] Basically I need to see the results from the function as 4 separate curves in 4 colours. Placing the "metric" function inside the Plot means that it plots everything as one function, which doesn't help (although it evaluates error free). In line with other answers on here (here and others) I recognise I have to either Evaluate it or Apply the metric to the Plot pure function, but then I get a Quantile error (and critical/"fall over" errors with some of the other more complex metrics I'm using). I've tried using default values, Holds, matching patterns on when perc doesn't exist etc etc but to no avail. I'm losing years off my life trying to get this to work so any help would be really appreciated... plotting evaluation share|improve this question asked Jan 8 '14 at 10:40 Adrian 183 add a comment| 2 Answers 2 active oldest votes up vote 2 down vote accepted Would you find this acceptable? data = RandomReal[10, {4, 1000}]; metric[