An Inequality Related the Zeros of Two Ordinary Bessel Functions
- 1 June 1985
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 19 (4) , 251-263
- https://doi.org/10.1080/00036818508839550
Abstract
AMS(MOS): 33A40, 47B05 Let v be real, v>-1 and v>Reμ, μ∊⊄ We prove an inequality which relates the first positive zero of the ordinary Bessel function Jv(z) and the absolute value of the real part of any zero of Jμ(z). Some lower bounds for the absolute value of the complex zeros of Jμ(z) follow immediately. In particular for μ real and μ>-1, this inequality proves that (1+v)-1ρv,1 is a strictly decreasing function in the interval -1v,1 is the first positive zero of Jv(z). A number of simple lower and upper bounds for the first positive zero of Jv(z) follow immediatly from this result.Keywords
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