[Maxima] Implementation of Gamma functions
toy.raymond at gmail.com
Fri Sep 5 23:55:07 CDT 2008
On Fri, Sep 5, 2008 at 5:56 PM, Dieter Kaiser <drdieterkaiser at web.de> wrote:
> I have started to implement support for the Incomplete Gamma function.
> only knows the symbols gammaincomplete and gammagreek.
> I have already finished the routines for the numerical evaluation of the
> Incomplete Gamma function for Float, Complex float and Bigfloat. Now I am
> working on the routines for Complex Bigfloats. I have used again an
> expansion in
> a series or continued fractions for the Regularized Incomplete Gamma
> Or we could use names like
> gamma_greek(a,z) = 1 - gamma_incomplete(a,z)
> gamma_incomplete_gen(a,z1,z2) =
> gamma_incomplete_reg(a,z) = gamma_incomplete(a,z)/gamma(a)
> gamma_incomplete_gen_reg(a,z1,z2)= gamma_incomplete_gen(a,z1,z2)/gamma(a)
I prefer these names. I find incomple and greek rather confusing because I
can never remember which one is the tail.
Maybe gamma_incomplete_tail for the integral from z to inf and
gamma_incomplete for the integral from 0 to z?
> Perhaps more interessting would be to implement a Log Gamma function and
> Inverse Gamma functions.
Well, gamma_incomplete gives us a way to evaluate erf, which we don't have
today for complex or bigfloat numbers.
Since we have a gamma function, the log gamma isn't too hard for numerical
evaluation. Inverse gamma is probably not too hard if a Newton iteration
can be applied.
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