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Bur. p.297. I don't have access to the Glaisher article. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. http://blogeurope.net/error-function/gauss-error-function-wiki.php

the integral $\int_x^\infty e^{-x^2}\mathrm dx$, well known for its use in physics, is so obviously suitable for the purpose, that, with the exception of receiving a name and a fixed notation, Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: erf error function (1) error function (0) Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Asymptotic expansion[edit] A useful asymptotic expansion of the complementary error function (and therefore also of the error function) for large real x is erfc ( x ) = e − Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; and Vetterling, W.T. "Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function." §6.2 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, https://en.wikipedia.org/wiki/Error_function

New York: Dover, pp.297-309, 1972. The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. Handbook **of Differential Equations, 3rd** ed.

An improved approximation for the Gaussian Q-function. Erfc Erfc is the complementary error function, commonly denoted , is an entire function defined by (1) (2) It is implemented in the Wolfram Language as Erfc[z]. Whittaker, E.T. Error Function Matlab Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end.

IEEE Transactions on Communications. 59 (11): 2939–2944. Error Function Calculator I'm not sure about the scaling with $\sqrt{2}$, though. –Mike Spivey May 8 '11 at 21:03 What about symmetry: $\text{erf}(x)$ is an odd function... –Fabian May 8 '11 at Browse other questions tagged probability statistics special-functions normal-distribution or ask your own question. http://mathworld.wolfram.com/Erf.html Some authors discuss the more general functions:[citation needed] E n ( x ) = n ! π ∫ 0 x e − t n d t = n ! π ∑

Hints help you try the next step on your own. Erf(inf) Is there **a Korean** word for 'Syllable Block'? Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: erf erfi x erfi (0) current community blog chat Mathematics Mathematics Meta your communities Sign Note that some authors (e.g., Whittaker and Watson 1990, p.341) define without the leading factor of .

Here's the relevant section of the paper: In 1871, J.W. http://mathworld.wolfram.com/Erfi.html Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Complementary Error Function This series diverges for every finite x, and its meaning as asymptotic expansion is that, for any N ∈ N {\displaystyle N\in \mathbb Γ 2 } one has erfc ( Error Function Table and Oldham, K.B. "The Error Function and Its Complement ." Ch.40 in An Atlas of Functions.

Soc. 3, 282-289, 1928. news For previous versions or for complex arguments, SciPy includes implementations of erf, erfc, erfi, and related functions for complex arguments in scipy.special.[21] A complex-argument erf is also in the arbitrary-precision arithmetic This directly results from the fact that the integrand e − t 2 {\displaystyle e^{-t^ − 2}} is an even function. Fortran 77 implementations are available in SLATEC. Inverse Error Function

All generalised error **functions for n>0** look similar on the positive x side of the graph. http://mathworld.wolfram.com/Erf.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Security Patch SUPEE-8788 - Possible Problems? have a peek at these guys Error function From Wikipedia, the free encyclopedia Jump to: navigation, search Plot of the error function In mathematics, the error function (also called the Gauss error function) is a special function

Wolfram|Alpha» Explore anything with the first computational knowledge engine. Erf(1) Hints help you try the next step on your own. asked 5 years ago viewed 8792 times active 5 years ago Linked 7 How can I evaluate $\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx$? 15 Motivation of the Gaussian Integral 6 Was the definition of $\mathrm{erf}$ changed

Sep 4 '11 at 13:42 Indeed, on page 296 of the Glaisher article, $x$ is used for both purposes. Interactive Entries>webMathematica Examples> History and Terminology>Wolfram Language Commands> Less... A two-argument form giving is also implemented as Erf[z0, z1]. Error Function Python New York: Chelsea, 1999.

Nevertheless, the Q-function can be approximated arbitrarily well as γ {\displaystyle \gamma } becomes larger and larger.[8] References[edit] ^ The Q-function, from cnx.org ^ a b Basic properties of the Q-function Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ( x 2 ) = 1 2 check my blog However, for −1 < x < 1, there is a unique real number denoted erf − 1 ( x ) {\displaystyle \operatorname Γ 0 ^{-1}(x)} satisfying erf ( erf