(HP65) Factorial and Gamma Function

[Dieter]

(10-22-2017 02:40 AM)Gamo Wrote:  Your quick modification is very good with more accurate approximation.

Here is an improved version. If uses a different technique to prevent overflow during the calculation of x^x · e^–x. In your program and my first version this is done with two consecutive multiplications of x^x/2, while now this term has been rearranged to (x/e)^x:

Code:

LBL A
8
EEX
4
1/x
CHS
STO 1
.
0
0
2
6
9
6
CHS
STO 2
2
8
8
1/x
STO 3
1
2
1/x
STO 4
CLX
RTN
LBL E
6
STO 0
STO/0
X<>Y
LBL 1
x>y?
GTO 2
1
+
STO*0
GTO 1
LBL 2
ENTER
ENTER
ENTER
1
CHS
e^x
*
X<>Y
Y^X
X<>Y
2
*
PI
*
SQRT
*
RCL 0
/
RCL 1
R↑
/
RCL 2
+
R↑
/
RCL 3
+
R↑
/
RCL 4
+
R↑
/
1
+
*
RTN

The program also no longer requires R5 and R6, most of the calculation is done on the stack.

Dieter