Abstract
A new algorithm is proposed for the evaluation of the Bessel function valuesJ p (x) with non-negative indexp and real positive argumentx. The basic ideas are the transfer of boundary conditions and the modified Prüfer transformation applied to Bessel equation. Special attention is paid to the accuracy of the interval reduction and the stability of the auxiliary initial value problems.
Zusammenfassung
Zur Berechnung der BesselfunktionswerteJ p (x) mit nichtnegativem Indexp und reellem Argumentx wird ein neuer Algorithmus empfohlen. Die Methode besteht aus der modifizierten Prüfer-Transformation der Besselschen Gleichung mit Übertragung der Randbedingungen. Besondere Aufmerksamkeit ist der Genauigkeit der Intervallreduktion und der Stabilität der Hilfsanfangswertprobleme gewidmet.
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Balla, K., Guk, O.S. & Vicsek, M. On the computation of Bessel functions of first kind. Computing 50, 77–85 (1993). https://doi.org/10.1007/BF02280041
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DOI: https://doi.org/10.1007/BF02280041