On the computation of modified Bessel function ratios

Gautschi, Walter; Slavik, Josef

doi:10.1090/S0025-5718-1978-0470267-9

On the computation of modified Bessel function ratios
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by Walter Gautschi and Josef Slavik PDF

Math. Comp. 32 (1978), 865-875 Request permission

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

D. E. Amos, S. L. Daniel, and M. K. Weston, CDC 6600 subroutines IBESS and JBESS for Bessel functions $I_{\nu }(x)$ and $J_{\nu }(x),$ $x\geq 0,$ $\nu \geq 0$, ACM Trans. Math. Software 3 (1977), no. 1, 76–92. MR 433810, DOI 10.1145/355719.355726
D. E. Amos, S. L. Daniel, and M. K. Weston, CDC 6600 subroutines IBESS and JBESS for Bessel functions $I_{\nu }(x)$ and $J_{\nu }(x),$ $x\geq 0,$ $\nu \geq 0$, ACM Trans. Math. Software 3 (1977), no. 1, 76–92. MR 433810, DOI 10.1145/355719.355726
Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002
Walter Gautschi, Anomalous convergence of a continued fraction for ratios of Kummer functions, Math. Comp. 31 (1977), no. 140, 994–999. MR 442204, DOI 10.1090/S0025-5718-1977-0442204-3
Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957 (German). MR 0085349
H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Co., Inc., New York, N. Y., 1948. MR 0025596