The HP-21S is another fine calculator from Hewlett-Packard's Pioneer series; it's a close relative to the HP-20S. However, unlike the HP-20S, which is still manufactured, the HP-21S is no longer in production.

There are to main differences between these calculators. First, scientific functions on the HP-20S, such as hyperbolic functions, unit conversions, or number base calculations are replaced with advanced statistical functions on the HP-21S; second, the set of built-in programs differs between the two machines.

Like the HP-20S, the HP-21S is also an algebraic calculator. A shame, really; algebraic entry just looks out of place on a fine HP instrument.

The keystroke programming model of the HP-21S is essentially identical to that of the HP-20S. Most keys are common between the two machines, so many programs are interchangeable. This is certainly true in the case of the Gamma function program example I wrote for the HP-20S.

Rather than repeating that program here, I have an alternative: the incomplete Gamma function. This program can also be used to approximate the Gamma function, by entering a high enough integration limit. For instance, 5 INPUT 50 XEQ A yields 24, which is the exact value of the Gamma function for the argument 5.

01 -   61 41 A	LBL A
02 -   21 1	STO 1
03 -   51 31	SWAP
04 -   21 2	STO 2
05 -   71	C
06 -   22 1	RCL 1
07 -   14	yx
08 -   22 2	RCL 2
09 -   45	÷
10 -   22 2	RCL 2
11 -   74	=
12 -   21 4	STO 4
13 -   21 3	STO 3
14 -   61 41 1	LBL 1
15 -   22 3	RCL 3
16 -   55	×
17 -   22 1	RCL 1
18 -   45	÷
19 -   1	1
20 -   21 75 2	STO+ 2
21 -   22 2	RCL 2
22 -   75	+
23 -   21 3	STO 3
24 -   22 4	RCL 4
25 -   21 5	STO 5
26 -   74	=
27 -   21 4	STO 4
28 -   65	-
29 -   22 5	RCL 5
30 -   74	=
31 -   61 43	x=0?
32 -   51 41 2	GTO 2
33 -   51 41 1	GTO 1
34 -   61 41 2	LBL 2
35 -   22 4	RCL 4
36 -   45	÷
37 -   22 1	RCL 1
38 -   12	ex
39 -   74	=
40 -   61 26	RTN