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Multiple complex zeros of derivatives of the cylindrical Bessel functions. (English) Zbl 0667.33006

Die Verf. betrachten zweifache Nullstellen der ersten Ableitung der zylindrischen Funktionen mit komplexem Index ν=α+iβ. Sie zeigen, daß J ν ' (z) für arg z[-π,π] nur reelle zweifache Nullstellen hat, dagegen Y ν ' (z) für arg z[0,π/2], arg ν[0,π/2] eine Folge von komplexen zweifachen Nullstellen hat, wo

α n =n+1/3+p/n -2/3 +o(n -2/3 ),β n =(n2)/2π-3p/n 2/3 +o(n -2/3 )·

Für arg ν[-π/2,0] hat die Funktion Y ν ' (ze -iπ ) solche Nullstellen. Ähnliche Untersuchungen werden für die Funktionen (H ν (1) (z) ' und K ν ' (z) geführt.

Reviewer: E.Riekstiņš
MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
30C15Zeros of polynomials, etc. (one complex variable)