HP 17BII+ and TI-84 Plus CE Python: Zeta Approximation
Zeta Function
zeta(x) = Σ(1 ÷ (n^x), n =1 to ∞)
We are going to use the approximation:
zeta(x) = Σ(1 ÷ (n^x), n =1 to w) where w = intg(10^((a + 2) ÷ x)
where a is the number of decimal places desired. The higher the accuracy, the longer the calculation takes. Also the lower x is, the longer the calculation takes.
This is for all x > 0.
HP 17BII+ Formula ZETA
ZETA=0×L(W:10^IP((ACC+2)÷X))+Σ(N:1:G(W):1:INV(N^X))
Examples:
ACC =3, X = 2; Result: ZETA = 1.63
ACC =3, X = 3.5; Result: ZETA = 1.13
ACC =3, X = 8.7; Result: ZETA = 1.00
TI-84 Plus CE Python: zeta.py
# 2021-12-07 ews
# zeta function approximation
from math import *
print("zeta function approximation")
x=eval(input("x? "))
a=eval(input("# places? "))
w=int(10**((a+2)/x)
z=0
n=1
while n<w:
z+=(n**x)**-1
n+=1
z=round(z,a)
print("zeta = "+str(z))
Eddie
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