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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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Keywords: Iterated coerror function, error function, coerror function, Mill’s ratio, probability integral
Article copyright: © Copyright 1973 American Mathematical Society