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The zeros of $az\sp 2 J{\sb \nu''}(z)+bzJ{\sb \nu'}(z)+cJ\sb \nu(z)$ as functions of order. (English) Zbl 0763.33002
{\it L. Lorch} and {\it P. Szego}, furthermore {\it R. Wong} and {\it T. Lang} have shown quite recently, in two connected papers on the positive zeros $j\sb{\nu k}{''}$ ($k=1,2,\dots$) of the Bessel function $J\sb \nu{''}(x)$, that $j\sb{\nu k}{''}$ is an increasing function of the order $\nu$ in the range $\nu>0$ [see {\it L. Lorch} and {\it P. Szego}, Can. J. Math. 42, No. 5, 933-948 (1990; Zbl 0716.33003) and ibid. 43, No. 3, 628-651 (1991; Zbl 0731.33001)]. The present note aims to extend the result just mentioned to positive zeros of an expression of the form $$az\sp 2 J\sb \nu{''}(z)+bzJ\sb \nu'(z)+cJ\sb \nu(z)$$ as function of $\nu$, where $a$, $b$, $c$ are certain real numbers subjected to suitable mild restrictions.

MSC:
 33C10 Bessel and Airy functions, cylinder functions, ${}_0F_1$
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