**Subject:** [Boost-bugs] [Boost C++ Libraries] #5113: math/special_functions/acosh.hpp wrong approximation for x near 1

**From:** Boost C++ Libraries (*noreply_at_[hidden]*)

**Date:** 2011-01-24 08:32:09

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#5113: math/special_functions/acosh.hpp wrong approximation for x near 1

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Reporter: SebastianLuther@â€¦ | Owner: johnmaddock

Type: Bugs | Status: new

Milestone: To Be Determined | Component: math

Version: Boost 1.45.0 | Severity: Problem

Keywords: |

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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/

-- Ticket URL: <https://svn.boost.org/trac/boost/ticket/5113> Boost C++ Libraries <http://www.boost.org/> Boost provides free peer-reviewed portable C++ source libraries.

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