search for: 1.53988

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) =

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;-x) / sqrt(x)

Something looks odd without your values (or the doc) because hypergeom_gain() should really approach 1 as x goes to infinity. But in the end, an approximation is probably OK because denoising is anything but an exact science :-) Jean-Marc Quoting John Ridges <jridges at masque.com>: > By my reckoning the confluent hypergoemetric functions should have the > following values: >

It's been a while since I did the maths. M(-.5;1;-x) optimises something else, though it's not too far. I think it may be [M(-.25;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: >

Thanks for the confirmation Jean-Marc. I kind of suspected from the comments that it was the confluent hypergoemetric function, which I was trying to evaluate using Kummer's equation, namely: M(a;b;x) is the sum from n=0 to infinity of (a)n*x^n / (b)n*n! where (a)n = a(a+1)(a+2) ... (a+n-1) But when I use Kummer's equation, I don't get the values in the "hypergeom_gain"