Bounds on iterated coerror functions and their ratios

Amos, D. E.

doi:10.1090/S0025-5718-1973-0331723-2

Bounds on iterated coerror functions and their ratios
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by D. E. Amos PDF

Math. Comp. 27 (1973), 413-427 Request permission

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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