Some inequalities for continued fractions
Author:
R. M. Dudley
Journal:
Math. Comp. 49 (1987), 585593
MSC:
Primary 40A15; Secondary 33A20, 65D20
MathSciNet review:
906191
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Abstract: For some continued fractions with mth convergent , it is shown that relative errors are monotone in some arguments. If all the entries and in Q are positive, then the relative error is bounded by , which is nonincreasing in the partial denominator for each , as is for . If for all , , and where and for j even, , then is bounded by , and both are nonincreasing in for even . These facts apply to continued fractions of Euler, Gauss and Laplace used in computing Poisson, binomial and normal probabilities, respectively, giving monotonicity of relative errors as functions of the variables in suitable ranges.
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 L. Euler, Opera Omnia, Ser. 1, Teubner, Leipzig and Berlin, Vols. 123, 19111938; Orell Füssli, Zürich, Vols. 2329, 19381956.
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 W. Gautschi, "Anomalous convergence of a continued fraction for ratios of Kummer functions," Math. Comp., v. 31, 1977, pp. 994999. MR 0442204 (56:590)
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 W. Gautschi, "A computational procedure for incomplete gamma functions," ACM Trans. Math. Software, v. 5, 1979, pp. 466481. MR 547763 (81f:65015)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819870906191X
PII:
S 00255718(1987)0906191X
Keywords:
Alternating continued fractions,
monotonicity of errors
Article copyright:
© Copyright 1987
American Mathematical Society
