hi, some identities for Pi, sum((3^(n+1/2)*(2*n)!*(2*cosh(2*x)+1)^(-n-1/2)*cosh((2*n+1)*x))/((4*n+2)*4^(2*n)*n!^2),n=0..inf)=Pi/6; sum(((2*n)!*(2*cosh(2*x)+sqrt(3))^(-n-1/2)*cosh((2*n+1)*x))/((4*n+2)*4^(2*n)*n!^2),n=0..inf)=Pi/12; sum((2^(1/4-(7*n)/2)*(2*n)!*(sqrt(2)*cosh(2*x)+1)^(-n-1/2)*cosh((2*n+1)*x))/((4*n+2)*n!^2),n=0..inf)=Pi/8; sum((3^(n+1/2)*(2*n)!*(2*cosh(2*x)-1)^(-n-1/2)*sinh((2*n+1)*x))/((4*n+2)*4^(2*n)*n!^2),n=0..inf)=Pi/6; sum(((2*n)!*(2*cosh(2*x)-sqrt(3))^(-n-1/2)*sinh((2*n+1)*x))/((4*n+2)*4^(2*n)*n!^2),n=0..inf)=Pi/12; sum((2^(1/4-(7*n)/2)*(2*n)!*(sqrt(2)*cosh(2*x)-1)^(-n-1/2)*sinh((2*n+1)*x))/((4*n+2)*n!^2),n=0..inf)=Pi/8; sum(((2*n)!*(2*cosh(t)+sqrt(2))^(n+1/2)*sech(2*t)^(n+1/2)*sinh((n+1/2)*t))/((2*n+1)*2^(4*n)*n!^2),n=0..inf)=Pi/4; Best regards