Lommel function

A Lommel differential equation is an ordinary differential equation. It is a generalization of the Bessel differential equation:

$z^{2}{\frac {d^{2}y}{dz^{2}}}+z{\frac {dy}{dz}}-(z^{2}-v^{2})y=kz^{\mu +1}$

A further generalization yields:

$z^{2}{\frac {d^{2}y}{dz^{2}}}+z{\frac {dy}{dz}}-(z^{2}-v^{2})y=\pm kz^{\mu +1}$

The solutions for these are given by the Lommel functions.

The second-order ordinary differential equation

$y''+g(y){y'}^{2}+f(x)y'=0$

is sometimes also called the Lommel differential equation.

See also

• Eugen von Lommel
• Lommel function
• Lommel polynomial

References

• Weisstein, Eric W. "Lommel Differential Equation." From MathWorld--A Wolfram Web Resource.