Dieter Kaiser wrote:
> 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)
>
>
Do we have a function to evaluate lower_gamma_incomplete? Using
gamma_incomplete is not very accurate if a is large and z is relatively
small (about 1) since we end up subtracting two numbers approximately
equal to gamma(a).
Ray