Am Montag, den 30.11.2009, 19:03 -0500 schrieb Raymond Toy:
> Current CVS says gamma_incomplete(1/2,0) is sqrt(%pi)/2. But the help
> for gamma_incomplete says gamma_incomplete(a,z) =
> integrate(exp(-t)*t^(a-1),t,0,z). (This matches A&S 6.5.2.)
>
> So from the documentation, I would expect the integral to be 0.
>
> Which is correct? Since A&S is our reference, I think the current value
> is incorrect and we should return 0.
Sorry, but I think the documentation is wrong. The problem is that the
Incomplete Gamma function and the lower Incomplete Gamma function are
easy to mix up. I think these are the defintions (e.g. wolfram.com)
Incomplete Gamma functions:
gamma_incomplete(a,z) = integrate(exp(-t)*t^(a-1),t,z,inf)
lower Incomplete Gamma function (gammagreek in Maxima):
lower_gamma_incomplete(a,z)= integrate(exp(-t)*t^(a-1),t,0,z)
Dieter Kaiser