The zeros of certain Lommel functions

Koumandos, Stamatis; Lamprecht, Martin

doi:10.1090/S0002-9939-2012-11139-6

The zeros of certain Lommel functions
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by Stamatis Koumandos and Martin Lamprecht PDF

Proc. Amer. Math. Soc. 140 (2012), 3091-3100 Request permission

Abstract:

Lommel’s function $s_{\mu ,\nu }(z)$ is a particular solution of the differential equation $z^{2}y'' + zy’ + (z^{2}-\nu ^{2})y = z^{\mu +1}$. Here we present estimates and monotonicity properties of the positive zeros of $s_{\mu -1/2,1/2}(z)$ when $\mu \in (0,1)$. The positivity of a closely related integral is also considered.

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