Gamma function differences?



#5

Hi to all!
I was just playing with my hp-42S and my newly arrived (and fixed!) HP-11C, and I found this difference:
In the Gamma function (in HP-11C shared with factorial [n!]) I found these results:

HP-11C: n = 68.5, result = 2.056343638e97

HP-42S: n = 68.5, result = 3.0019615151e95

HP-11C: n = 67.5, result = 3.00196151e95

HP-42S: n = 67.5, result = 4.44735039275e93

HP-11C: n = 66.5, result = 4.447350392e93

Commodore SR4190: n = 68.5, result = 3.00196151995e95

Commodore SR4190: n = 67.5, result = 4.44735039501e93


I'm just curious (as I don't have the HP-11C user's manual): the argument for Gamma function in the HP-11C is added by 1 internally?

Regards,

Nelson


#6

Dude, gamma(x)=(x-1)!
To calculate gamma(68.5) on your 11c, you need calculate the factiorial of 67.5 to get 3.001961515*10^95 (which is what you got for for your "n=67.5" except for the last decimal; I multiplied the result of 67.5! by 1e-95 to display all the digits.)
On a side note, the results of your 42s match my 48gx and 49g.
I hope this clarifies the discrepancy.

Sincerely,

Brandon


#7

This is because the gamma function in HP-11C is "hidden" in the factorial function? The use of the same key is clever, but as I said I don't have the manual, and I really forgot about the gamma(n) = (n-1)! equivalence...

Thanks!

Best regards,

Nelson


#8

Viktor Toth has a good discussion of the gamma function at rskey.org:

http://www.rskey.org/gamma.htm


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