(12C Platinum) GAMMA FUNCTION
07-03-2019, 07:58 AM (This post was last modified: 07-03-2019 08:42 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 508 Joined: Dec 2016
(12C Platinum) GAMMA FUNCTION
This program was adapted form HP-19C Solutions Handbook page 31

[Reference: Gamma Function, John Ulissides. "65 Notes," V 3 N 10, p. 37.]

As stated in the handbook this program approximates the gamma
function for 0<X≤61 with eight digit accuracy over most of the range.

In this case this program use less PI significant digit than the 19C build in PI
function so this program will give out the most to five digit accuracy.

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Equation:

GAMMA(x) = e [LN(√2Pi/X) + X (LN(X) - X + A)]

Where A = [1- 1/30(X^2) + 1/105(X^4))(1/12(X))]

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Example: FIX 5

1!
1 [R/S] display 1.00000

0.5!
.5 [R/S] display 1.77245

5.25!
5.25 [R/S] display 35.21161

7!
7 [ENTER] 1 [+] display 8 [R/S] display 5040.00021

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Program: HP-12C Platinum on RPN mode
Code:
 001 STO 0 002  3 003  5 004  5 005 ENTER 006  1 007  1 008  3 009  ÷ 010 STO 2 ------------ 011 RCL 0 012  9 013  + 014 ENTER 015 1/x 016 X^2 017 ENTER 018 X^2 019  3 020  , 021  5 022  ÷ 023  - 024  3 025  0 026  ÷ 027  1 028  - 029 X<>Y 030  1 ----------- 031  2 032  x 033  ÷ 034  + 035 X<>Y 036 ENTER 037 LN 038  x 039  - 040 X<>Y ------------ 041 RCL 2 042  ÷ 043  2 044  ÷ 045 √x 046 LN 047  + 048 CHS 049 e^x 050 STO 1 ----------- 051 CLx 052  9 053  - 054 STO÷1 055  1 056  + 057 X<>Y 058 X≤Y 059 GTO 062 060 X<>Y 061 GTO 054 062 RCL 1

Gamo
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