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,,