Erfi

Author

Eric W. Weisstein
January 25, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/Erfi.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Erfi.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Plots

<<Utilities`Plot`

Real Axis

Plot[Erfi[x],{x,-2,2},PlotStyle->Red,AxesLabel->{x,Erfi[x]}]

Complex Plane

ComplexPlot3D[Erfi[z],{z,-2,2},PlotPoints->100]//Timing

ComplexContourPlot[Erfi[z],{z,-2,2}]//Timing

Derivative

D[Erfi[z],z]

Integral

Integrate[Erfi[z],z]

Series

Series[Erfi[z],{z,0,20}]

V4.2

Series[Erfi[z],{z,∞,12}]

...wrong...

V5.0

Series[Erfi[z],{z,∞,12}]

...wrong...

V5.1

Series[Erfi[z],{z,∞,12}]

V5.2

Series[Erfi[z],{z,∞,12}]

V7

Series[Erfi[z],{z,∞,12}]

Series[Erfi[z],{z,∞,12},Assumptions->Arg[z]≤0]

ser=Series[Erfi[z],{z,∞,3},Assumptions->Arg[z]>0]

Normal[I+(E^(z^2)) ((1/((Sqrt[π]) z))+(1/(2 (Sqrt[π]) (z^3)))+((O[(1/z)])^4))]/.z->9.+I

Normal[-I+(E^(z^2)) ((1/((Sqrt[π]) z))+(1/(2 (Sqrt[π]) (z^3)))+((O[(1/z)])^4))]/.z->9.+I

http://functions.wolfram.com/GammaBetaErf/Erfi/06/02/