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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Bounds on iterated coerror functions and their ratios


Author: D. E. Amos
Journal: Math. Comp. 27 (1973), 413-427
MSC: Primary 65D20
MathSciNet review: 0331723
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Abstract: Upper and lower bounds on $ {y_n} = {i^n}\;{\operatorname{erfc}}(x)$ and $ {r_n} = {y_n}/{y_{n - 1}}, n \geqq 1, - \infty < x < \infty $, are established in terms of elementary functions. Numerical procedures for refining these bounds are presented so that $ {r_n}$ and $ {y_k},k = 0,1, \ldots ,n$, can be computed to a specified accuracy. Some relations establishing bounds on $ r'_{n}$ and $ r''_{n}$ are also derived.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0331723-2
PII: S 0025-5718(1973)0331723-2
Keywords: Iterated coerror function, error function, coerror function, Mill's ratio, probability integral
Article copyright: © Copyright 1973 American Mathematical Society