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Not exactly knowing what kind of Texas Instrument calculator you possess, I would recommend that you purchase a brand new one unless you can find a broken one of the same kind and use it as a test to disassemble and check the glass.
Let us first call each thing by its name. If you are looking for the Gamma function , the one defined by the integral from 0 to infinity of t^(n-1) *e^(-t), look no further. It it does not exist on your scientific calculator. However, if you are looking for the factorial function ( the !) then you can access it by pressing [SHIFT][x^-1].
It is true that the Gamma function reduces to the factorial function when its argument is a positive integer, but I do not believe we should use the names indiscriminately. Sorry if that ruffles some feathers.
Are you serious? No calculator purchase should be solely based on such a trivial matter. But if you are looking for a very good scientific calculator, I would suggest the new Write View EL-W506/W516/W546 calculators by Sharp, or the FX-115ES/991ES Natural Display by Casio.
With these calculators you can see what you enter displayed as in textbooks. Naturally, they all do coordinates conversions from Polar to Rectangular and from Rectangular to Polar.
If you want to do that do not buy an 83 or 83+. all the 84's and all the 89's come with usb chords so you can hook them up to the computer, now how you do that i don't know cause i use an 83. You would have to do more research. I hope this can help. GOOD LUCK
The closest I could come up with was the operations manual from the predecessor model IV. It contains lots of examples, not simple key usage.
Go to this page and look for the link just below the words "PRODUCT DETAILS"
"Beta tester of "0"s and "1's"