Advertisement Autoplay When autoplay is enabled, a suggested video will automatically play next. Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: erf error function (1) error function (0) TOPICS ABOUT HOMECALCULATORS Academics Arts Automotive Beauty Loading... Schöpf and P.

Both functions are overloaded to accept arguments of type float, double, and long double. However, it can be extended to the disk |z| < 1 of the complex plane, using the Maclaurin series erf − 1 ( z ) = ∑ k = 0 Category Education License Standard YouTube License Show more Show less Loading... Despite the name "imaginary error function", erfi ( x ) {\displaystyle \operatorname 8 (x)} is real when x is real.

Perl: erf (for real arguments, using Cody's algorithm[20]) is implemented in the Perl module Math::SpecFun Python: Included since version 2.7 as math.erf() and math.erfc() for real arguments. Similarly, (8) (OEIS A103979 and A103980). It is also called the Gauss error function or probability integral. Sign in to add this video to a playlist.

Up next The Error Function - Duration: 9:54. Mathematical Methods for Physicists, 3rd ed. Toggle Main Navigation Log In Products Solutions Academia Support Community Events Contact Us How To Buy Contact Us How To Buy Log In Products Solutions Academia Support Community Events Search MATLAB W.

poysermath 419,943 views 11:23 Integrating e^(-x^2) The Gaussian Integral - Duration: 1:30. Acton, F.S. New York: Chelsea, 1948. PARI/GP: provides erfc for real and complex arguments, via tanh-sinh quadrature plus special cases.

It is an entire function defined by (1) Note that some authors (e.g., Whittaker and Watson 1990, p.341) define without the leading factor of . Orlando, FL: Academic Press, pp.568-569, 1985. Cambridge, England: Cambridge University Press, 1990. Another approximation is given by erf ( x ) ≈ sgn ( x ) 1 − exp ( − x 2 4 π + a x 2 1

New York: Dover, pp.179-182, 1967. Havil, J. Wolfram Language» Knowledge-based programming for everyone. The inverse of erf has several interesting derivative and integral properties. © Had2Know 2010 How to Find the Great Circle Distance Between Two Points on a Sphere Gamma & Log Gamma

p.297. doi:10.3888/tmj.16–11.Schöpf, Supancic ^ E. It is also called the Gauss error function or probability integral. Similarly, the En for even n look similar (but not identical) to each other after a simple division by n!.

Whittaker, E.T. Supancic, "On Bürmann's Theorem and Its Application to Problems of Linear and Nonlinear Heat Transfer and Diffusion," The Mathematica Journal, 2014. For , (5) where is the incomplete gamma function. Also has erfi for calculating i erf ( i x ) {\displaystyle i\operatorname {erf} (ix)} Maple: Maple implements both erf and erfc for real and complex arguments.

Math. Sign in 29 8 Don't like this video? Properties[edit] Plots in the complex plane Integrand exp(−z2) erf(z) The property erf ( − z ) = − erf ( z ) {\displaystyle \operatorname − 6 (-z)=-\operatorname − 5 This feature is not available right now.

Your cache administrator is webmaster. MR0167642. Watson, G.N. "Theorems Stated by Ramanujan (IV): Theorems on Approximate Integration and Summation of Series." J. Emerson © 2010 Skip navigation UploadSign inSearch Loading...

M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008). Another form of erfc ( x ) {\displaystyle \operatorname 2 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 All generalised error functions for n>0 look similar on the positive x side of the graph. 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

Java: Apache commons-math[19] provides implementations of erf and erfc for real arguments. You can also select a location from the following list: Americas Canada (English) United States (English) Europe Belgium (English) Denmark (English) Deutschland (Deutsch) España (Español) Finland (English) France (Français) Ireland (English) The error function is defined as: Error Function Table The following is the error function and complementary error function table that shows the values of erf(x) and erfc(x) for x ranging 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 ,

Numerical Methods That Work, 2nd printing.