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Monotonicity properties of the zeros of Bessel functions

Published online by Cambridge University Press:  17 February 2009

Roger C. McCann  and
E. R. Love
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Abstract

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Let jν, denote the first positive zero of Jν. It is shown that jν/(ν + α) is a strictly decreasing function of ν for each positive α provided ν is sufficiently large. For each α lowe bounds on ν are given to assure the monotonicity of jν/(ν + α). From this it is shown that jν > ν + j0 for all ν > 0, which is both simpler and an improvement on the well known inequality Jν ≥ (ν (ν + 2))1/2.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 1 , July 1982 , pp. 67 - 85
Copyright
Copyright © Australian Mathematical Society 1982

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