Ince Polynomials

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

:$w^+\xi\sin(2z)w^+(\eta-p\xi\cos(2z))w=0. \,$

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

:
$w(z)=Ce^(e^\mp 1)$

where $C$ is a constant.

See also

* Whittaker–Hill equation
* Ince–Gaussian beam

References

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*{{dlmf, id=28.31, title=Equations of Whittaker–Hill and Ince, first=G. , last=Wolf
Ordinary differential equations