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Zbl 0773.33003
Lorch, Lee
Some inequalities for the first positive zeros of Bessel functions. (English)
[J] SIAM J. Math. Anal. 24, No.3, 814-823 (1993). ISSN 0036-1410; ISSN 1095-7154/e

The author establishes the following lower bounds $$\align j\sp 2 &> (\nu+1)(\nu+5), \qquad -1<\nu<\infty,\\ j\sp 2 &> {{24(\nu+1)\sp 2} \over {1-2\nu+\sqrt{(2\nu+3)(2\nu+11)}}} -2(\nu\sp 2-1), \quad - 1<\nu<\infty,\endalign$$ where $j$ denotes the first positive zero of the Bessel function $J\sb \nu(x)$. The paper is motivated by the need of these inequalities for some authors in order to prove the Payne-Pólya- Weinberger conjecture.
[A.Laforgia (Potenza)]

MSC 2000:: *33C10 Cylinder functions, etc.

Keywords: zero; Bessel function; inequalities

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