# [Maxima] Implementation of Gamma functions

Kostas Oikonomou ko at research.att.com
Sat Sep 6 18:22:20 CDT 2008

```> gamma_incomplete(a,z)
> gamma_incomplete_generalized(a,z1,z2)
> gamma_incomplete_regularized(a,z)
> gamma_incomplete_generalized_regularized(a,z1,z2)

I think these are good choices.   Having used Mathematica
for a long time, I have experienced the usefulness of long,
descriptive names for functions or other entities that are
not frequently used.
And having a convention for how to order the parts of a long
name is also very helpful to the user.

> Yes, gamma_greek is the most confusing name and perhaps we should avoid the use
> of this function. The Maxima symbol gammagreek is only used in the code of
> specint and perhaps could be completely eliminated.

That would be ok by me.

> The biggest problem is that it is not always clear what is meant by the
> Incomplete Gamma function. A&S gives three different definitions with the
> formulas 6.5.1, 6.5.2 and 6.5.3 but do not distinguish the definitions with
> different names.
> The names I have suggested follow the conventions of functions.wolfram.com.
> There we have the following definition for the Incomplete Gamma function which
> is equal to A&S 6.5.3:
>
> Gamma(a,z) = (exp(-t)*t^(a-1),t,x,inf)   (upper tail, Upper case Greek gamma)
>
> A very important feature of this definition is that the interconnections between
> a lot of special functions can be expressed more easy and directly with this
> definition of the Incomplete Gamma function.

I'm used to the Wolfram/Mathematica definitions, even though
they don't fully agree with A&S.
I have also found the regularized versions quite useful, and
I'm glad to see you including them in Maxima.

Kostas
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