The zeros of certain Lommel functions
Date
2012Source
Proceedings of the American Mathematical SocietyVolume
140Issue
9Pages
3091-3100Google Scholar check
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Lommel's function s μ,ν(z) is a particular solution of the differential equation z 2y″ + zy′ + (z 2 - ν 2)y = z μ+1. Here we present estimates and monotonicity properties of the positive zeros of s μ-1/2,1/2(z) when μ ∈ (0, 1). The positivity of a closely related integral is also considered. © 2012 American Mathematical Society.