Formula 26 a := (sqrt(exp(2*Pi)-exp(Pi)+1)*sqrt(exp(2*Pi)+exp(Pi)+1)*sqrt(exp(8*Pi)+exp(2*Pi)+1)*sqrt(exp(12*Pi)+exp(10*Pi)+exp(8*Pi)+exp(6*Pi)+2*exp(4*Pi)-2*exp(2*Pi)+1))/(sqrt(5)*exp(4*Pi)+sqrt(5)*exp(2*Pi)+sqrt(5)); b:= -(a/2)+(exp(12*Pi)+exp(10*Pi)+exp(8*Pi)+exp(6*Pi)-1)/(2*(exp(4*Pi)+exp(2*Pi)+1)); Golden ratio phi:=a/(b+1/(1+exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+ exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+…)))))))))))))); Formula 27 a:=(sqrt(exp(2*Pi)+exp(Pi)+1)*sqrt(exp(3*Pi)+exp(2*Pi)+1)*sqrt(exp(5*Pi)-exp(4*Pi)+exp(2*Pi)-exp(Pi)+1)*sqrt(exp(10*Pi)+exp(9*Pi)+exp(7*Pi)+exp(5*Pi)+exp(4*Pi)+exp(3*Pi)-2*exp(2*Pi)+1))/(sqrt(5)*exp(3*Pi)+sqrt(5)*exp(2*Pi)+sqrt(5)); b:= -(a/2)+(exp(10*Pi)+exp(9*Pi)+exp(7*Pi)+exp(5*Pi)+ exp(4*Pi)-exp(3*Pi)-1)/(2*(exp(3*Pi)+exp(2*Pi)+1)); Golden ratio phi:=a/(b+1/(1+exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+ exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+…)))))))))))))); Formula 28 a:=(sqrt(24*exp(6*Pi)+12*exp(5*Pi)+4*exp(4*Pi)+2*exp(3*Pi)+7*exp(2*Pi)-2*exp(Pi)+1)*sqrt(24*exp(6*Pi)+12*exp(5*Pi)+4*exp (4*Pi)+2*exp(3*Pi)+7*exp(2*Pi)+2*exp(Pi)+1))/(6*sqrt(5)*exp(2*Pi)+3*sqrt(5)*exp(Pi)+sqrt(5)) ; b:= -(a/2)+ (24*exp(6*Pi)+12*exp(5*Pi)+4*exp(4*Pi)+2*exp(3*Pi)-5*exp(2*Pi)-1)/(2*(6*exp(2*Pi)+3*exp(Pi)+1)); Golden ratio phi:=a/(b+1/(1+exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+ exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+…)))))))))))))); Formula 29 cos(k*exp(x))*cos(k*exp(-x))=(sum((-1)^(n)*k^(2*n)*cosh(2*n*x)/(2*n)!,n=0..infinity))^2-(sum((-1)^(n)*k^(2*n)*sinh(2*n*x)/(2*n)!,n=0..infinity))^2;