Bounds on iterated coerror functions and their ratios

Author:
D. E. Amos

Journal:
Math. Comp. **27** (1973), 413-427

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1973-0331723-2

MathSciNet review:
0331723

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Abstract | References | Similar Articles | Additional Information

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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*Math. Comp.*, v. 22, 1968, p. 454.

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Additional Information

Keywords:
Iterated coerror function,
error function,
coerror function,
Mill’s ratio,
probability integral

Article copyright:
© Copyright 1973
American Mathematical Society