lower incomplete gamma as gamma(a,0,x)

[kcrisman]

See #16697 - apparently some systems implement this.

Depends on #16697

CC: @paulmasson

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/17722

[sagetrac-buck]

comment:1

This interface makes a lot of sense to me.

The upper incomplete gamma would then be gamma(a,x,oo).
With the third arg defaulting to oo, the upper incomplete could be written as just gamma(a, x), compatible with current code.
gamma(a) would be equivalent to gamma(a, 0, oo).

The identity at work is this one:

[rwst]

Dependencies: #16697

[sagetrac-buck]

comment:3

How should the gamma api look once this is complete?

Will gamma_inc_lower exist? If so, will it normalize itself to gamma(a, 0, x)? If not, should we block #16697 on this work?

Will gamma(a, 0, x) emit latex for lower-gamma?