Elsasser Function

Author

Eric W. Weisstein
January 2, 2008

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

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Definition

Elsasser[y_,u_,opts___]:=Integrate[Exp[-2Pi y u Sinh[2Pi y]/(Cosh[2Pi y]-Cos[2Pi x])],{x,-1/2,1/2},opts]

Elsasser[y,u,Assumptions->y>0&&u>0]//Timing

Elsasser[y,u]//Timing

Table[Elsasser[i,u],{i,0,2}]//Timing

Table[Elsasser[y,i],{i,0,2}]//Timing

Plot

Plot3D[Evaluate[Elsasser[y,u]],{y,0,2},{u,0,2},AxesLabel->{y,u}]

Integrate[Exp[-2Pi y u Sinh[2Pi y]/(Cosh[2Pi y]-Cos[2Pi x])],{x,-1/2,1/2}]

Plot3D[NIntegrate[Exp[-2Pi y u Sinh[2Pi y]/(Cosh[2Pi y]-Cos[2Pi x])],{x,-1/2,1/2}],{y,0,2},{u,0,2},AxesLabel->{y,u}]