and Watson, G.N. Wall, H.S. Integrals and Series, Vol.2: Special Functions. I have learned that integrals of this form can't be solved the usual way, but can be evaluated in terms of the error function.

Washington, DC: Math. calculus integration definite-integrals special-functions error-function share|cite|improve this question edited Apr 27 '14 at 18:34 asked Jun 9 '12 at 13:26 petru 108118 add a comment| 2 Answers 2 active oldest votes Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end.

Sequences A000079/M1129, A001147/M3002, A007680/M2861, A103979, A103980 in "The On-Line Encyclopedia of Integer Sequences." Spanier, J. Products & Services Mathematica Mathematica Online Development Platform Programming Lab Data Science Platform Finance Platform SystemModeler Enterprise Private Cloud Enterprise Mathematica Wolfram|Alpha Appliance Enterprise Solutions Corporate Consulting Technical Services Wolfram|Alpha Business share|cite|improve this answer edited Jul 4 '14 at 19:45 answered May 14 '14 at 4:18 Mhenni Benghorbal 39.7k52966 add a comment| up vote 1 down vote This integral is $I=\sqrt{\pi\sigma^2}\cdot E(X^n)$ Why did it take 10,000 years to discover the Bajoran wormhole?

Please try the request again. c n − i + 1 x i {\displaystyle \int x^ 7e^ 6\;\mathrm 5 x={\frac 4 3}x^ 2e^ 1-{\frac 0 θ 9}\int x^ Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: erf error function (1) error function (0) SolitaryRoad.com Website owner: James Miller [ Home ] See also npdf(), which gives the probability density.

A two-argument form giving is also implemented as Erf[z0, z1]. Examples Some basic values and limits: >>> from mpmath import * >>> mp.dps = 25; mp.pretty = True >>> fresnels(0) 0.0 >>> fresnels(inf) 0.5 >>> fresnels(-inf) -0.5 >>> fresnels(1) 0.4382591473903547660767567 >>> Olds, C.D. For , (5) where is the incomplete gamma function.

More precisely, \[\mathrm{erf}(x) = \frac{2}{\sqrt \pi} \int_0^x \exp(-t^2) \,dt\] Basic examples Simple values and limits include: >>> from mpmath import * >>> mp.dps = 15; mp.pretty = True >>> erf(0) 0.0 Chapman and Hall/CRC Press. Series: Monographs and Research Notes in Mathematics. The case with \(n = 1\) is also given by e1().

Here is a nice formula in terms of a friendly function, the gamma function $$ I = \frac{\mu^n\sigma}{2}\sum_{k=0}^{n}((-1)^k+1){n\choose k}\left(\frac{\sigma}{\mu}\right)^k \Gamma\left(\frac{k}{2}+\frac{1}{2} \right),$$ where ${n\choose k}=\frac{n!}{k!(n-k)!}$ and $\Gamma(x)$ is the gamma function. Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume II. Retrieved 2016-02-12. Cambridge, England: Cambridge University Press, 1990.

more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science a n + 1 ( n = 0 , 1 , 2 , … , a > 0 ) {\displaystyle \int _{0}^{\infty }x^{n}e^{-ax}\,\mathrm {d} x={\begin{cases}{\dfrac {\Gamma (n+1)}{a^{n+1}}}&(n>-1,a>0)\\\\{\dfrac {n!}{a^{n+1}}}&(n=0,1,2,\ldots ,a>0)\end{cases}}} ∫ 0 Documentation Feedback Please complete this field. How do I help minimize interruptions during group meetings as a student?

Translate Error and Exponential Integral Functions Error functions, trigonometric and hyperbolic integral functions, Fresnel and Dawson integrals MuPAD Functions erf Error function erfc Complementary error function erfi Imaginary error function inverf Soc. 3, 282-289, 1928. Havil, J. Players stopping other player actions House of Santa Claus Security Patch SUPEE-8788 - Possible Problems?

Incomplete gamma functions¶ gammainc()¶ mpmath.gammainc(z, a=0, b=inf, regularized=False)¶ gammainc(z, a=0, b=inf) computes the (generalized) incomplete gamma function with integration limits \([a, b]\): \[\Gamma(z,a,b) = \int_a^b t^{z-1} e^{-t} \, dt\] The generalized Hints help you try the next step on your own. By using this site, you agree to the Terms of Use and Privacy Policy. A simple integral involving erf that Wolfram Language cannot do is given by (30) (M.R.D'Orsogna, pers.

Learn how» Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index Interactive Entries Random The Ei-function is related to the more general family of exponential integral functions denoted by \(E_n\), which are available as expint(). London Math. Sloane, N.J.A.

Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. This function avoids cancellation that occurs when naively computing the complementary error function as 1-erf(x): >>> from mpmath import * >>> mp.dps = 15; mp.pretty = True >>> 1 - erf(10) comm., May 9, 2004). II (1 ed.).

Generated Sat, 15 Oct 2016 12:16:04 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection For real \(x\), the Ei-function behaves roughly like \(\mathrm{Ei}(x) \approx \exp(x) + \log(|x|)\).