The TI-55 is one of the lower-end early Texas Instruments LED programmable calculators. My first encounter with this calculator was on the pages of a Texas Instruments book on microprocessor technology, a translation of which was published in Hungary in 1980 or thereabouts.

Lower-end or not, the TI-55 is still a decent little programmable calculator. In addition to the usual set of scientific and statistical functions, it has ten memory registers and 32 steps of program memory. (Registers 8 and 9 correspond with program steps 17-24, and 25-32, respectively, whereas registers 1-7 may be used by the built-in statistical functions.)

The most significant shortcoming of the TI-55 is the near complete lack of program control instructions. There is no GOTO, no conditional tests, nothing. However, the calculator's RST instruction, plus the fact that program execution stops when an error occurs, can be used to implement simple loops¹.

The limited capacity of this calculator does not make it possible to implement a complex algorithm like that of the Gamma function. However, a simple factorial program loop is certainly within the capabilities of this machine (well, yes, there's a built-in factorial function but where's the fun in using that?) Because the only way to stop a program conditionally is by generating an error condition (which displays the blinking value of 9.9999999e99), it is not possible to cause the result to be displayed when the program ends; it must be retrieved instead from memory (CLR RCL 0).

00 51	STO
01 01	1
02 34	1/x
03 61	RCL
04 01	1
05 55	×
06 51	STO
07 00	0
08 43	(
09 61	RCL
10 01	1
11 65	-
12 01	1
13 44	)
14 87	RST

Perhaps more elegant is to compute an approximation of the factorial using Stirling's formula. This method requires no iteration or conditional execution, so it's more suited for use with the TI-55. Here is a program that approximates the natural logarithm of the factorial (so it can be used for arguments greater than 69). This program is actually fairly accurate; calculating the factorial of 5 yields 119.99 instead of 120, for instance, which is not bad at all.

00 51    STO
01 00    0
02 55    ×
03 02    2
04 55    ×
05 49    π
06 85    =
07 23    lnx
08 45    ÷
09 02    2
10 75    +
11 61    RCL
12 00    0
13 55    ×
14 23    lnx
15 65    -
16 61    RCL
17 00    0
18 75    +
19 43    (
20 61    RCL
21 00    0
22 34    1/x
23 45    ÷
24 01    1
25 02    2
26 75    +
27 01    1
28 44    )
29 23    lnx
30 85    =
31 86    R/S

¹One might suspect that as it is possible for a program to write into program memory by storing numbers in registers 8 and 9, it might be possible to implement conditional constructs using this method. Unfortunately, not all keycodes can be stored in program memory this way (and, it appears, some of the most important keycodes like R/S or RST, cannot), which severely limits the utility of this programming method. However, see this article by Claus Buchholz, which provides intriguing details.