For , (5) where is the incomplete gamma function. Both functions are overloaded to accept arguments of type float, double, and long double. The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ( x 2 ) = 1 2 The relationship between the error function erf and normcdf is normcdf(x)=12(1−erf(−x2)).For expressions of the form 1 - erf(x), use the complementary error function erfc instead.

Negative integer values of Im(ƒ) are shown with thick red lines. Numerical Methods That Work, 2nd printing. M. Assoc.

J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. This is useful, for example, in determining the bit error rate of a digital communication system. For more information, see Tall Arrays.TipsYou can also find the standard normal probability distribution using the Statistics and Machine Learning Toolbox™ function normcdf. For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079).

If L is sufficiently far from the mean, i.e. μ − L ≥ σ ln k {\displaystyle \mu -L\geq \sigma {\sqrt {\ln {k}}}} , then: Pr [ X ≤ L If you're going the Taylor series route, the best series to use is formula 7.1.6 in Abramowitz and Stegun. IDL: provides both erf and erfc for real and complex arguments. For , may be computed from (9) (10) (OEIS A000079 and A001147; Acton 1990).

xrealnumber 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt Privacy Policy Terms of use FAQ Contact us © 2016 CASIO COMPUTER CO., LTD. Olds, C.D. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. Aug 29 '10 at 23:07 add a comment| 4 Answers 4 active oldest votes up vote 9 down vote accepted I am assuming that you need the error function only for

See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF). Erf is implemented in the Wolfram Language as Erf[z]. Sequences A000079/M1129, A001147/M3002, A007680/M2861, A103979, A103980 in "The On-Line Encyclopedia of Integer Sequences." Spanier, J. Using the alternate value a≈0.147 reduces the maximum error to about 0.00012.[12] This approximation can also be inverted to calculate the inverse error function: erf − 1 ( x )

Prudnikov, A.P.; Brychkov, Yu.A.; and Marichev, O.I. ISBN0-486-61272-4. Referenced on Wolfram|Alpha: Erf CITE THIS AS: Weisstein, Eric W. "Erf." From MathWorld--A Wolfram Web Resource. Arfken, G.

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 At the imaginary axis, it tends to ±i∞. As for the problem that the language your writing in has no such library already: for me that is probably not as big of a deal as you think. Erf is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function).

ERF(x) returns the error function integrated between zero and x. up vote 9 down vote favorite 2 I am looking for an accurate algorithm to calculate the error function I have tried using the following formula, (Handbook of Mathematical Functions, formula Another approximation is given by erf ( x ) ≈ sgn ( x ) 1 − exp ( − x 2 4 π + a x 2 1 To let the software define the Y-axis automatically, leave both input fields for the Y-axis empty.

The denominator terms are sequence A007680 in the OEIS. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. 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) Springer-Verlag.

Integrals and Series, Vol.2: Special Functions. Despite the name "imaginary error function", erfi ( x ) {\displaystyle \operatorname 5 (x)} is real when x is real. The inverse error function is usually defined with domain (−1,1), and it is restricted to this domain in many computer algebra systems. Why (in universe) are blade runners called blade runners?

Related functions[edit] The error function is essentially identical to the standard normal cumulative distribution function, denoted Φ, also named norm(x) by software languages, as they differ only by scaling and translation. With modern technology, is it possible to permanently stay in sunlight, without going into space? Erf can also be defined as a Maclaurin series (6) (7) (OEIS A007680). Negative integer values of Im(ƒ) are shown with thick red lines.

Java: Apache commons-math[19] provides implementations of erf and erfc for real arguments. The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. If you size it properly, then the function will appear constant with respect to your machine precision outside of this interval. Exploded Suffixes Implementation of a generic List Are leet passwords easily crackable?

M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008). Another form of erfc ( x ) {\displaystyle \operatorname {erfc} (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 )