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Zeros of generalized Airy functions. (English) Zbl 0562.30007
Some interlacing properties of the zeros of the generalized Airy functions A 1 (z,p) are given for non-positive integral values of p. The result that A 1 (z,p) has no real zero for p> is extended to show that all the zeros of A 1 (z,p) are real and simple if p<. It is also shown that all the zeros of the functions B k (z,p,1) for k=1,2,3 are simple for non-positive integral p.
MSC:
30C15Zeros of polynomials, etc. (one complex variable)
33C10Bessel and Airy functions, cylinder functions, 0 F 1