Gamma(x+1) (0 <= x <= 39.4)01 STO 0 24 RCL 2

02 . 25 y^x

03 6 26 /

04 y^x 27 STO+ 3

05 1 28 1

06 9 29 STO+ 2

07 * 30 GTO 12

08 STO 1 31 RCL 3

09 0 32 2

10 STO 2 33 SQRTx

11 STO 3 34 LASTx

12 RCL 2 35 /

13 RCL 1 36 /

14 x<=y 37 2

15 GTO 31 38 ENTER

16 x<>y 39 LN

17 2 40 /

18 * 41 RCL 0

19 1 42 1

20 + 43 +

21 RCL 0 44 y^x

22 y^x 45 /

23 2 46 GTO 0012.12 R/S => 648,976,950.1 after 3.5 seconds (HP-12C+)

On the 15C,

12.12 x! => 648,976,950.9

This is based on the following approximation I've come up with:

Gamma(x+1) ~ SUM(k=0,inf,(2*k+1)^x/2^k)/(sqrt2/2*(2/ln(2))^(x+1))

Obviously, this is not the proper way to compute the Gamma function. It's just an example of what can be done on the fast 12C+. Just for an idea, it would take about 7 minutes to compute Gamma(40) on a normal 12C using this method.

Gerson.

--------------

The approximation is being used reversely, that is, it is meant to approximate

this integer sequence, not the Gamma function:

an ~ n!/(2*sqrt2)*(2/ln(2))^(n+1)

I found it when thinking about John Smitherman's math joke turned into a problem. The numbers 2, 6, 34, 294... (which showed as the problem was getting progressively more complex) ought to mean something... I couldn't find it at OEIS but I found 1, 3, 17, 147..., the halved sequence. Eventually I found out the original sequence is the row sums of Sierpinski-Pascal-MacMahon triangle, whatever this might be.

Next time someone starts a joke I'll try to just laugh, as everybody else :-)

I just intended to put a computationally intensive programming problem to the 12C+ to see how it performed. For computing Gamma function on the 12C+ or the normal 12C and 12c Platinum there isn't anything better than Egan Ford's program:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv016.cgi?read=100275

See message #6.

*Edited: 26 June 2009, 10:30 a.m. *