Kelvin Differential Equation

Author

Eric W. Weisstein
February 17, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/KelvinDifferentialEquation.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Checks

DSolve[z^2 D[w[z],{z,2}]+z D[w[z],z]-(I z^2+ν^2) w[z]==0,w[z],z]//TraditionalForm

FullS

Function[w,z^2 D[w,{z,2}]+z D[w,z]-(I z^2+ν^2) w]/@{ KelvinBer[ν,z]+ I KelvinBei[ν,z],
KelvinBer[-ν,z]+I KelvinBei[-ν,z],
KelvinKer[ν,z]+I KelvinKei[ν,z],
KelvinKer[-ν,z]+I KelvinKei[-ν,z]
}//FullSimplify