id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
5113	math/special_functions/acosh.hpp wrong approximation for x near 1	SebastianLuther@…	John Maddock	"The documentation and the code have different bugs for the approximation of acosh(x) for x near 1.

First of all they use different definitions of y. The documentation has y=1-x and the code has y=x-1. They both use the formula
{{{(1+(1/12)*y+(3/160)*y^2)*sqrt(2*y)}}}, but neither of them is correct.

correct formulas [1]

{{{y=1-x -> (1+(1/12)*y+(3/160)*y^2)*sqrt(-2*y)}}}

{{{y=x-1 -> (1-(1/12)*y+(3/160)*y^2)*sqrt(2*y)}}}

[1] http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/"	Bugs	closed	Boost 1.47.0	math	Boost 1.45.0	Problem	fixed