[math-fun] some easy little formulas ...

Hello some easy little formulas .. Pi=4*product((16384*n^2*(2*n-1)^3*(4*n+1)^4)/((2*n+1)*(8*n-3)^4*(8*n+1)^4),n=1..infinity); 1/sqrt(Pi)=(8/(Gamma(1/4))^2)*product(((4*n+1)^2-1)/(4*n+1)^2,n=1..infinity); 1/sqrt(Pi)=(8/(m*(Gamma(1/4))^2))*sum((1-(k/m)^4)^(1/4),k=1..m-1); (Pi)^(3/2)=(4*((Gamma(3/4))^2/(m)))*sum((1-(k/m)^4)^(1/4),k=1..m-1); (Pi)^(3/2)=(4*(Gamma(3/4))^2)*product(((4*n+1)^2-1)/(4*n+1)^2,n=1..infinity); Pi=((Gamma(1/4))^4/64)*(1+sum(((-1)^(n)/(4*n+1))*((2*n-1)!)/(2^(2*n-1)*(n!)*((n-1)!)),n=1..infinity))^(-2); (Pi)^3=(16*(Gamma(3/4))^4)*(1+sum(((-1)^(n)/(4*n+1))*((2*n-1)!)/(2^(2*n-1)*(n!)*((n-1)!)),n=1..infinity))^(2); Best regards