TI 84 Plus CE TI-Basic and TI Nspire CX II Python: Gamma by Multiplication Recursion Property
Introduction
The program calculates the gamma function for any real positive number in tenths by the multiplication recursion:
Γ(x + 1) = x * Γ(x)
For example:
Γ(2.5)
= 1.5 * Γ(1.5)
= 1.5 * 0.5 * Γ(0.5)
≈ 1.5 * 0.5 * 1.772453851
≈ 1.329340388
Reduce x by 1 until 1 is in between 0.1 and 1.
Gamma Values:
Γ(0.1) = 9.513507699
Γ(0.2) = 4.590843712
Γ(0.3) = 2.991568988
Γ(0.4) = 2.218159544
Γ(0.5) = 1.772453851
Γ(0.6) = 1.489192249
Γ(0.7) = 1.298055333
Γ(0.8) = 1.164229714
Γ(0.9) = 1.068628702
Γ(1) = 1
TI-84 Plus CE Program: GAMMATEN
TI-Basic
Notes:
* To get the small L to create lists with custom names, get the character with the key strokes: [ 2nd ] ( list ), OPS, B. L. In this listing, I will write L^ to symbolize the lower case L.
* L^TEN is a custom list.
Program listing:
{9.513507699, 4.590843712, 2.991568988,
2.218159544, 1.772453851, 1.489192249,
1.298055333, 1.164229714, 1.068628702
1}→L^TEN
ClrHome
Disp "GAMMA X (NEAREST 0.1)"
Input "X≥0.1, X?",X
round(X,1)→X
fPart(X)*10→F
If F=0:10→F
1→G
While X>1
G*(X-1)→G
X-1→X
End
G*L^TEN(F)→G
Disp "EST. GAMMA: ", G
TI-NSpire Python Script: gammaten.py
The code is defined as a function.
def gammaten(x):
lten=[9.513507699]
lten.append(4.590843712)
lten.append(2.991568988)
lten.append(2.218159544)
lten.append(1.772453851)
lten.append(1.489192249)
lten.append(1.298055333)
lten.append(1.164229714)
lten.append(1.068628702)
lten.append(1)
#print("gamma(x) to the nearest 0.1")
x=round(x,1)
f=round(10*(x-int(x))-1)
g=1
while x>1:
x-=1
g*=x
g*=lten[f]
return [g,f]
# list[-1] gets last item too
# round integers for accurate results!
# 2022-06-13 EWS
Eddie
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
