An approximate inverse for atanh(x)/x
- From: David W. Cantrell <DWCantrell@xxxxxxxxxxx>
- Date: 09 Jul 2006 03:03:57 GMT
Recently, in another newsgroup, someone wanted to solve an equation
equivalent to atanh(x)/x = c for x, given some c >= 1. Presumably of
course, that cannot be done in closed form in terms of familiar functions.
However, there is an approximation which is reasonably accurate,
considering its simplicity:
For the equation atanh(x)/x = c, the nonnegative solution for x is
approximately
sqrt(1 - exp((1 - c)(2 + 1/c)))
with |error| < 0.0009 for all c >= 1.
David W. Cantrell
.
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