Higher derivatives of the Bessel functions with respect to the order. (English) Zbl 1351.33005
In this paper, the author presents closed expressions for the first derivatives w.r.t. the order of Bessel functions \(J_{v}(z)\) and its modified version \(I_{v}(z),\) Macdonald functions \(K_{v}(z)\), Neumann functions \(Y_{v}(z) \) and Kelvin functions for any value of the order \(v.\) In general case, the representation of derivatives of any order is given in terms of Kampé de Fériet function. Later on, the author derives the formula for the second derivative of \(J_{v}(z)\) at integer points \(v=\pm n\) and gives the expressions which correspond to related functions. Finally, the author gives an example of a closed expression for the third derivative at integer points.
Reviewer: Gumrah Uysal (Karabuk)
MSC:
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
References:
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| [2] | DOI: 10.1007/978-3-662-11761-3 · doi:10.1007/978-3-662-11761-3 |
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