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On the derivatives of the Bessel and Struve functions with respect to the order. (English) Zbl 1070.33003
Using known expressions of first derivatives with respect to order $\nu$, of Bessel functions at $\nu=\pm n$, $n=0,1,...$ $\nu=\pm 1/2$ and Struve functions at $\nu=\pm 1/2$, the authors derive closed form expressions for the first derivatives with respect to order $\nu$ of Bessel functions $J_{\nu}(z)$, $Y_{\nu}(z)$, $I_{\nu}(z)$, $K_{\nu}(z)$ at $\nu=\pm n \pm 1/2$ $n=0,1,...$, the integral Bessel functions $Ji_{\nu}(z)$, $Yi_{\nu}(z)$, $Ki_{\nu}(z)$ at $\nu=\pm n$ $n=0,1,...$ and Struve functions $H_{\nu}(z)$, $L_{\nu}(z)$ at $\nu=\pm n \pm 1/2$ and $\nu=n$ $n=0,1,...\ \ .$

33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
33C20Generalized hypergeometric series, ${}_pF_q$
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