Modified Struve Function

Author

Eric W. Weisstein
May 20, 2004

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

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

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

Plots

<<Utilities`Plot`
<<Utilities`Typesetting`

Real Axis

Plot[Evaluate[Table[StruveL[n,z],{n,0,5}]],{z,-10,10},PlotStyle->{Black,Red,Yellow,Green,Blue,Violet},AxesLabel->TraditionalForm/@{x,StruveL[n,x]}]

Complex Plane

ComplexPlot3D[StruveL[0,z],{z,-5,5}]//Timing

ComplexContourPlot[StruveL[0,z],{z,-5,5}]//Timing

Sums

((((z/2)))^(ν+1))(∑_(k=0)^∞)(((((z/2)))^(2 k))/((Gamma[k+(3/2)]) (Gamma[k+ν+(3/2)])))==(StruveL[ν, z])

((((1/2)z))^(ν+1))Sum[(((((1/2)z))^(2k))/(Gamma[k+(3/2)]Gamma[k+ν+(3/2)])),{k,0,∞}]

Identities

(StruveL[n, z])==-i exp(-(1/2) π i n) (StruveH[n, i z])

FullSimplify[Subtract@@{StruveL[n,z],-I*Exp[-n*Pi*I/2]*StruveH[n,I z]}]

Subtract@@@Table[{StruveL[n,z],-I*Exp[-n*Pi*I/2]*StruveH[n,I z]}/.{n->Random[Complex],z->Random[Complex]},{10}]//Chop