https://svn.boost.org/trac10/ticket/4583 <p> 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... </p> <p> IMO the formula should be corrected as follows: </p> <ol class="loweralpha"><li>Multiply the series by a factor '1/a' so that it matches the expansion of the lower incomplete gamma function on page 238 </li><li>The continued fraction in the example above evaluates to something near 1.14, but Gamma(0.5, 0.5)/sqrt(2*e) = </li></ol><p> 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: <a class="ext-link" href="http://functions.wolfram.com/06.06.10.0008.01"><span class="icon">​</span>http://functions.wolfram.com/06.06.10.0008.01</a> </p> <p> But why don't you simply use the formula implemented in the boost sources?? </p> <p> Cheers </p> <p> Wolf Lammen </p> <p> BTW, ticket <a class="closed ticket" href="https://svn.boost.org/trac10/ticket/4518" title="#4518: Bugs: boost_1_44_beta_pdf, math.pdf (closed: fixed)">#4518</a> is not fully served (still a typo present). </p> en-us /htdocs/site/boost.png https://svn.boost.org/trac10/ticket/4583 Trac 1.4.3 ookami1@… Sun, 22 Aug 2010 05:50:57 GMT https://svn.boost.org/trac10/ticket/4583#comment:3 https://svn.boost.org/trac10/ticket/4583#comment:3 <ul> <li><strong>status</strong> <span class="trac-field-old">new</span> → <span class="trac-field-new">closed</span> </li> <li><strong>resolution</strong> → <span class="trac-field-new">fixed</span> </li> </ul> <p> (In <a class="changeset" href="https://svn.boost.org/trac10/changeset/64962" title="Correct equations used for generic version of tgamma - equations ...">[64962]</a>) Correct equations used for generic version of tgamma - equations should now match those used for igamma and the actual code. Fixes <a class="closed ticket" href="https://svn.boost.org/trac10/ticket/4583" title="#4583: Bugs: boost_1_44_beta_pdf, math.pdf (closed: fixed)">#4583</a>. </p> Ticket John Maddock Mon, 23 Aug 2010 09:04:09 GMT