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A continued fraction approximation of the modified Bessel function \(I_ 1(t)\). (English) Zbl 0734.41020

The authors use a continued fraction approach in approximating the function \(f(s)=s+1-(s(s+2))^{1/2}.\)

MSC:

41A21 Padé approximation
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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References:

[1] Jones, W. B.; Thron, W. J., Continued Fractions, Analytic Theory and Applications (1980), Addison-Wesley · Zbl 0445.30003
[2] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1970), Dover · Zbl 0515.33001
[3] Murphy, J¿A.; O’Donohoe, M. R., Some properties of continued fractions with applications in Markov processes, J. Inst. Math. Applics., 16, 57-71 (1975) · Zbl 0314.65057
[4] O. Perron, Die Lehre von den Kettenbrüchen; O. Perron, Die Lehre von den Kettenbrüchen
[5] Gragg, W. B.; Harrod, W. J., The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math., 44, 317-335 (1984) · Zbl 0556.65027
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