Chudnovsky algorithm
08-17-2021, 02:50 AM
Post: #1
 compsystems Senior Member Posts: 1,382 Joined: Dec 2013
Chudnovsky algorithm
PI_ (n):=((2.0*sqrt(2)/9801)*Σ((4*k)!*
(1103+26390*k)/((k!)^4*396^(4*k)),k,0,n))^(-1);

Why the evaluation at different values of n doesn't change the decimal values?

PI_ (1) [enter] 3.14159265359
PI_ (10) [enter] 3.14159265359
PI_ (34) [enter] 3.14159265359
08-17-2021, 04:30 AM
Post: #2
 Valentin Albillo Senior Member Posts: 1,100 Joined: Feb 2015
RE: Chudnovsky algorithm
(08-17-2021 02:50 AM)compsystems Wrote:  PI_ (n):=((2.0*sqrt(2)/9801)*Σ((4*k)!*
(1103+26390*k)/((k!)^4*396^(4*k)),k,0,n))^(-1);

Why the evaluation at different values of n doesn't change the decimal values?

PI_ (1) [enter] 3.14159265359
PI_ (10) [enter] 3.14159265359
PI_ (34) [enter] 3.14159265359

First of all, this is one of Ramanujan formulae for computing Pi.

Secondly, you're not getting changes because just 1 term of the series already gives the accuracy your system allows. Use some multiprecision system and you'll see them change. Estas matando moscas a cañonazos.

V.

All My Articles & other Materials here:  Valentin Albillo's HP Collection

 « Next Oldest | Next Newest »