Ince equation

In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation

$w^{\prime \prime }+\xi \sin (2z)w^{\prime }+(\eta -p\xi \cos (2z))w=0.$

When p is a non-negative integer, it has polynomial solutions called Ince polynomials. In particular, when $p=1,\eta \pm \xi =1$, then it has a closed-form solution

$w(z)=C{e}^{-iz}(e^{2iz}\mp 1)$

where $C$ is a constant.

See also

• Whittaker–Hill equation
• Ince–Gaussian beam

References

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