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Monotonicity properties of zeros of generalized Airy functions. (English) Zbl 0681.33008

The generalized Airy function is a solution of the differential equation

(1)y '' +x α y=0,x[0,),

where α is a positive number. From the introduction: “M. S. P. Eastham conjectured that the first positive zero a α1 of a solution of (1) with y(0)=0, decreases as α increases. We show here that this decrease (to 1) occurs for all positive zeros of such a solution and indeed for all, except possibly the first of the zeros of any nontrivial solution of (1) even without the condition y(0)=0·

Reviewer: L.Littlejohn

MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
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