The HP-41C was the first in a revolutionary new line of calculators by Hewlett-Packard. In addition to its large memory and an unprecendentedly rich set of internal functions, the machine offered an alphanumeric display, and perhaps most importantly, extreme versatility in the form of four expansion ports. With these ports, the HP-41C became much more than a mere calculator; it became a superbly flexible computing platform. In addition to being a dream machine to many a student around the world, the HP-41C found its way to the most unusual places, including the US military or the cockpit of the famous supersonic Concorde airliner.

And if the almost fearsomely rich set of functions offered by the HP-41C or its many expansion modules wasn't enough, the HP-41C was also a hacker's dream: "synthetic programming", as it was called, opened up whole new vistas for the adventurous programmer who wished to explore undocumented instructions, internal functions, and more.

As a programming example, I previously wrote a Gamma function implementation for the HP-41CX. Although this implementation fits into the smaller memory of the HP-41C, the fit is somewhat tight; you need to use the SIZE 009 command to create enough space in program memory, leaving only 9 data registers for other purposes.

So instead, here's another way to calculate the Gamma function: using the incomplete Gamma function algorithm which, although somewhat slower, requires a lot less room. To use the program below, enter the argument and an integration limit; e.g., 5 ENTER 40 yields exactly 24.

01	LBL'IG
02	STO 01
03	X<>Y
04	STO 02
05	Y^X
06	RCL 02
07	/
08	STO 03
09	LBL 01
10	RCL 01
11	RCL 02
12	1
13	+
14	STO 02
15	/
16	RCL 03
17	*
18	STO 03
19	+
20	X!=Y?
21	GTO 01
22	RCL 01
23	E^X
24	/
25	RTN