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The roots of $J\sb 0(z)-iJ\sb 1(z)=0$. (English) Zbl 0695.33006
Für die, in Anwendungen auftretende Linearkombination von Besselschen Funktionen: $$ f(z):=J\sb 0(z)-{\frak i}J\sb 1(z) $$ wird eine Tafel für die ersten 30, betragsmäßig kleinsten Nullstellen, die sämtlich in der Halbebene: Im z$<0$ liegen, mit einer Genauigkeit der Ordnung $O(10\sp{-6})$ aufgestellt, und zwar aufbauend auf Reihenentwicklung und asymptotischer Entwicklung von f(z) unter numerischer Verbesserung der Näherungswerte durch Newton-Raphsonsche Iteration.
Reviewer: L.Neckermann

33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$