[math-fun] Pi: acceleration of the speed of convergence

Hello, dear all Here are two formulas of Pi, the first is convergence 2 * n + 1 And the second 2 * n + 3 The formulas converge to an odd multiple of Pi depending on the x [0] taken, for example x[0]=3 ; x[m+1]=x[m]+sum(2*(n!)^2*sin(k*x[m])/(k*(n+k)!*(n-k)!),k=1..n); x[m+1]=x[m]+((2*n+1)!)^2/(2^(4*n-1)*(n!)^2)*sum(cos((2*k+1)*x[m]/2)/((2*k+1)^2*(n-k)!*(n+k+1)!),k=0..n); The two formulas are particular cases of thousands of formulas of this form of which I have been able to highlight. Their transformation into linear convergence can allow me to reach 500 decimal places in each calculation. Best Regards... FME...