Pi par la m\303\251thode des Chudnovsky.
with(gfun) :
with(NumGfun) :
A, B, C := 13591409, 545140134, 640320^3 ;
rec[Pi] := { (A+B*n)*(3*n+3)*(3*n+2)*(3*n+1)*(n+1)^3*C * u(n+1) + (6*n+6)*(6*n+5)*(6*n+4)*(6*n+3)*(6*n+2)*(6*n+1)*(A+B*(n+1)) * u(n), u(0) = 12*A } ;
ti := time() :
x := fnth_term(rec[Pi], u(n), 5000, 50001, 'series') :
evalf[50001](sqrt(C)/x) ;
time() - ti ;
ti := time() :
x := fnth_term(rec[Pi], u(n), 10000, 100001, 'series') :
evalf[100001](sqrt(C)/x) :
time() - ti ;
ti := time() :
x := fnth_term(rec[Pi], u(n), 20000, 200001, 'series') :
evalf[200001](sqrt(C)/x) :
time() - ti ;
ti := time() :
x := fnth_term(rec[Pi], u(n), 40000, 400001, 'series') :
evalf[400001](sqrt(C)/x) :
time() - ti ;
ti := time() :
x := fnth_term(rec[Pi], u(n), 80000, 800001, 'series') :
evalf[800001](sqrt(C)/x) :
time() - ti ;