[Boost-bugs] [Boost C++ Libraries] #4583: boost_1_44_beta_pdf, math.pdf

Subject: [Boost-bugs] [Boost C++ Libraries] #4583: boost_1_44_beta_pdf, math.pdf
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2010-08-21 20:32:10

#4583: boost_1_44_beta_pdf, math.pdf
----------------------------+-----------------------------------------------
 Reporter:  ookami1@…       |       Owner:  johnmaddock
     Type:  Bugs            |      Status:  new        
Milestone:  Boost-1.45.0    |   Component:  math       
  Version:  Boost 1.44.0    |    Severity:  Problem    
 Keywords:                  |  
----------------------------+-----------------------------------------------
 I'm afraid, both the general formulas for Gamma(a) on p. 224 and ln
 Gamma(z) on p.227 are not correct. I gave the formula on p.224 a try,
 using a = 0.5 and l = 0.5.
 Using the 5th approximant, the limit of the continued fraction can be
 constrained to the intervall between 58/51 and 394/345. The series
 evaluated to 5th order yields 253/105 with an error between 0 and 0.003.
 Entering the upper limits into the formula on p. 224 gives an upper bound
 of 1.525 for Gamma(0.5), which is known to be sqrt(pi) = 1.77...

 IMO the formula should be corrected as follows:
 a. Multiply the series by a factor '1/a' so that it matches the expansion
 of the lower incomplete gamma function on page 238
 b. The continued fraction in the example above evaluates to something near
 1.14, but Gamma(0.5, 0.5)/sqrt(2*e) =
 erfc(sqrt(0.5))*sqrt(pi/(2*e)) = 1.311... So it seems the continued
 fraction incorrect either. The closest I could find in the internet is
 here:

 http://functions.wolfram.com/06.06.10.0008.01


 But why don't you simply use the formula implemented in the boost
 sources??

 Cheers

 Wolf Lammen

 BTW, ticket #4518 is not fully served (still a typo present).

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/4583>
Boost C++ Libraries <http://www.boost.org/>
Boost provides free peer-reviewed portable C++ source libraries.