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On the computation of modified Bessel function ratios


Authors: Walter Gautschi and Josef Slavik
Journal: Math. Comp. 32 (1978), 865-875
MSC: Primary 33A40
DOI: https://doi.org/10.1090/S0025-5718-1978-0470267-9
MathSciNet review: 0470267
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Abstract: A detailed comparison is made between a continued fraction of Gauss, and one of Perron, for the evaluation of ratios of modified Bessel functions $ {I_v}(x)/{I_{v - 1}}(x),x > 0$, $ v > 0$. It will be shown that Perron's continued fraction has remarkable advantages over Gauss' continued fraction, particularly when $ x > > v$.


References [Enhancements On Off] (What's this?)

  • [1] D. E. AMOS, S. L. DANIEL & M. K. WESTON, "CDC 6600 subroutines IBESS and JBESS for Bessel functions $ {I_v}(x)$ and $ {J_v}(x),x \geqslant 0,v \geqslant 0$," ACM Trans. Math. Software, v. 3, 1977, pp. 76-92. MR 0433810 (55:6781)
  • [2] D. E. AMOS, S. L. DANIEL & M. K. WESTON, "Algorithm 511-CDC 6600 subroutines IBESS and JBESS for Bessel functions $ {I_v}(x)$ and $ {J_v}(x),x \geqslant 0,v \geqslant 0$," ACM Trans. Math. Software, v. 3, 1977, pp. 93-95. MR 0433810 (55:6781)
  • [3] W. GAUTSCHI, "Computational aspects of three-term recurrence relations," SIAM Rev., v. 9, 1967, pp. 24-82. MR 0213062 (35:3927)
  • [4] W. GAUTSCHI, "Anomalous convergence of a continued fraction for ratios of Kummer functions," Math. Comp., v. 31, 1977, pp. 994-999. MR 0442204 (56:590)
  • [5] O. PERRON, Die Lehre von den Kettenbrüchen, vol. II, 3rd ed., Teubner Verlag, Stuttgart, 1957. MR 0085349 (19:25c)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0470267-9
Article copyright: © Copyright 1978 American Mathematical Society

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