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Zbl 0802.33004
Matviyenko, Gregory
On the evaluation of Bessel functions. (English)
[J] Appl. Comput. Harmon. Anal. 1, No.1, 116-135 (1993). ISSN 1063-5203

The author presents an algorithm for the evaluation of Bessel functions $J\sb \nu(x)$, $Y\sb \nu(x)$ and $H\sb \nu\sp{(j)}(x)$ $(j=1,2)$ of arbitrary positive orders and arguments. This algorithm consists of two parts: One of them combines the evaluation of the function $H\sb \nu\sp{(1)}(x)$ via Taylor expansions and via numerical computation of the Sommerfield integral along contours of steepest descents (the Debye contours); the other one computes $H\sb \nu\sp{(1)} (x)$ by means of the Debye asymptotic expansions.\par The algorithm can be easily implemented for the evaluation of $J\sb \nu(x)$, $Y\sb \nu(x)$ and $H\sb \nu\sp{(2)} (x)$ making use of the well- known connection formulas between the three kinds of Bessel functions.
[N.Hayek (La Laguna)]

MSC 2000:: *33C10 Cylinder functions, etc.
65D20 Computation of special functions

Keywords: Bessel functions; steepest descents; Debye asymptotic expansions

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