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I got the approximation from a Google book: http://books.google.com/books?id=2CAqsF-RebgC&pg=PA385 Page 392, formula (10.33) Using this formula, you're right, hypergeom_gain() would *not* converge to 1 for large x, but would instead be gamma(1.25)/sqrt(sqrt(x)) which would approach zero. Now if the formula for the hypergeometric gain were instead gamma(1.5) * M(-.5;1;...

...;1;-x)]^2 (or is it the sqrt?) that is supposed to be there. In any case, if there's a mismatch between the doc and the code, the code is the one likely to be correct. Jean-Marc John Ridges a ?crit : > I got the approximation from a Google book: > > http://books.google.com/books?id=2CAqsF-RebgC&pg=PA385 > > Page 392, formula (10.33) > > Using this formula, you're right, hypergeom_gain() would *not* converge > to 1 for large x, but would instead be gamma(1.25)/sqrt(sqrt(x)) which > would approach zero. Now if the formula for the hypergeometric gain were &g...

By my reckoning the confluent hypergoemetric functions should have the following values: M(-.25;1;-.5) = 1.11433 M(-.25;1;-1) = 1.21088 M(-.25;1;-1.5) = 1.29385 M(-.25;1;-2) = 1.36627 M(-.25;1;-2.5) = 1.43038 M(-.25;1;-3) = 1.48784 M(-.25;1;-3.5) = 1.53988 M(-.25;1;-4) = 1.58747 M(-.25;1;-4.5) = 1.63134 M(-.25;1;-5) = 1.67206 M(-.25;1;-5.5) = 1.71009 M(-.25;1;-6) = 1.74579 M(-.25;1;-6.5) =