Monotonicity properties of the zeros of Bessel functions
- 1 July 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 24 (1) , 67-85
- https://doi.org/10.1017/s0334270000003325
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- Lower Bounds for the Zeros of Bessel FunctionsProceedings of the American Mathematical Society, 1977