The HP-22S belongs to the Pioneer series of Hewlett-Packard's line of calculators. Although it is a close relative to the HP-20S and HP-21S, it is not a keystroke-programmable machine; instead, it has a built-in "SOLVE" function that lets you enter equations in algebraic form and solve for unknown variables. Since this SOLVE feature also has the capability to evaluate formulae, this makes the HP-22S technically a programmable machine; you can enter a mathematical expression which is then stored permanently in the calculator's continuous memory, and you can evalute the expression at a later time.

Whereas some other Hewlett-Packard calculators with a similar SOLVE feature offer special functions for conditional execution or loops, these functions are not present in the HP-22S. Therefore, this calculator is limited to more straightforward formulae. That said, I was suprised to find that the machine has sufficient storage for an implementation of my favorite example, the Gamma function, with plenty of memory to spare.

G=SQRT(2×π)÷X×(1.00000000019+
   76.1800917295÷(X+1)-86.5053203294÷(X+2)+
   24.0140982408÷(X+3)-1.23173957245÷(X+4)+
   1.20865097387E-3÷(X+5)-5.39523938495E-6÷(X+6))×
   (X+5.5)^(X+.5)÷EXP(X+5.5)

Looks ugly, but it works! Better yet, thanks to the built-in SOLVE feature, we automatically get an inverse Gamma function as well. Instead of specifying X and solving for G, you can specify G and solve for X; for instance, you can determine that the Gamma function's value is exactly 100 for 5.89251869634.