Elliptic Exponential Function

Author

Eric W. Weisstein
June 27, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheoreticFunctions/EllipticExponentialFunction.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Plots

Plot[{EllipticExp[u,{1,1}][[1]],EllipticExp[u,{1,1}][[2]],Sqrt[#^2]/#&[EllipticExp[u,{1,1}][[2]]]},{u,-5,5},PlotRange->{-5,5},PlotStyle->{Red,Violet,Blue},
AxesLabel->TraditionalForm/@{u,(Subscript[eexp, 1,1])[u]}]

f[z_?NumericQ]:=EllipticExp[z,{1,1}][[1]]

ComplexPlot3D[f[u],{u,-5-5I,5+5I},PlotPoints->100,ComplexPlotLabel->(Subscript[eexp, 1,1])[u]]//Timing

ComplexContourPlot[f[u],{u,-5-5I,5+5I},ComplexPlotLabel->(Subscript[eexp, 1,1])[u]]//Timing

g[z_?NumericQ]:=EllipticExp[z,{1,1}][[2]]

ComplexPlot3D[g[u],{u,-5-5I,5+5I},PlotPoints->100,ComplexPlotLabel->(Subscript[eexpy, 1,1])[u]]//Timing

ComplexContourPlot[g[u],{u,-5-5I,5+5I},ComplexPlotLabel->(Subscript[eexpy, 1,1])[u]]//Timing