austern@ux5.lbl.gov (Matt Austern) (02/04/91)
The gamma function is one of the standard "special functions" of
complex analysis. It is therefore a little bit frustrating to see
that the gamma function on the HP 48 only accepts real arguments.
(Not that I'm complaining, of course: HP is the only company I know
of that puts the gamma function on its calculators at all.)
The following program corrects this. The algorithm isn't as accurate
as that on the HP 48, but it still is quite good: better than 1 part
in 10^9.
This program uses an algorithm from Numerical Recipes. (Press, et.
al.) They give no theory behind the algorithm, besides the obvious
observation that it asymptotically approaches Stirling's
approximation, but they do give a reference. It is only valid for
Re (z) > 1, so I use the "reflection formula" if given an argument
with Re(z) < 1.
You'll note that this program calls itself (in the reflection
formula), so you should either store it under the name GAMMA or
change that call.
%%HP: T(3)A(R)F(.);
\<< \-> z1
\<< z1 1 - \-> z
\<<
IF z RE 0 <
THEN \pi \->NUM z
* DUP SIN / 1 z -
GAMMA /
ELSE z 5.5 +
z .5 + ^ z 5.5 +
NEG EXP * 2 \pi \->NUM
* \v/ * 1 76.18009173
z 1 + / +
-86.50532033 z 2 +
/ + 24.01409822 z 3
+ / + -1.231739516
z 4 + / +
.00120858003 z 5 +
/ + -.00000536382 z
6 + / + *
END
\>>
\>>
\>>
--
Matthew Austern austern@lbl.bitnet Proverbs for paranoids, 3: If
(415) 644-2618 austern@lbl.gov they can get you asking the wrong
questions, they don't have to worry
about answers.sowa@amdew.llnl.gov (Erik C. Sowa) (02/05/91)
In article <9483@dog.ee.lbl.gov>, austern@ux5.lbl.gov (Matt Austern) writes: >From: austern@ux5.lbl.gov (Matt Austern) >The gamma function is one of the standard "special functions" of >complex analysis. It is therefore a little bit frustrating to see >that the gamma function on the HP 48 only accepts real arguments. >(Not that I'm complaining, of course: HP is the only company I know >of that puts the gamma function on its calculators at all.) >This program uses an algorithm from Numerical Recipes. (Press, et. Hooray! A program of use to practicing scientists and engineers! And it's on the scale appropriate for a (fancy and powerful) pocket calculator. Abramowitz and Stegun is also invaluable for these kinds of special functions. I only wish they would publish a "portable" edition w/o those numerical tables which an hp48sx can easily reproduce. Just say NO to interpolation... -- erik sowa (sowa@amdew.llnl.gov,sowa@cms1.llnl.gov) I'm not stupid. I've even heard of Harvey Mudd College. In fact, they gave me a degree. Big deal. It's what you do with your education that counts.