Hello.... I noted that : abs(sqrt(1-x^2)/acos(x))=((x+1)/2)*(1/2+1/sqrt(2+2*x))*(1/2+1/sqrt(2+sqrt(2+2*x)))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*x)))) *(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*x)))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*x)))))) * cdots ; abs(x/asin(x))=((sqrt(1-x^2)+1)/2)*(1/2+1/sqrt(2+2*sqrt(1-x^2)))*(1/2+1/sqrt(2+sqrt(2+2*sqrt(1-x^2))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*sqrt(1-x^2))))) *(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*sqrt(1-x^2)))))) *cdots ; abs(x/asinh(x))=((sqrt(1+x^2)+1)/2)*(1/2+1/sqrt(2+2*sqrt(1+x^2)))*(1/2+1/sqrt(2+sqrt(2+2*sqrt(1+x^2))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*sqrt(1+x^2))))) *(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*sqrt(1+x^2)))))) *cdots ; abs((x/sqrt(1+x^2))*(1/atan(x)))=((1/sqrt(1+x^2)+1)/2)*(1/2+1/sqrt(2+2*(1/sqrt(1+x^2))))*(1/2+1/sqrt(2+sqrt(2+2*(1/sqrt(1+x^2)))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*(1/sqrt(1+x^2))))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*(1/sqrt(1+x^2))))))) * cdots ; abs((x/sqrt(1-x^2))*(1/atanh(x)))=((1/sqrt(1-x^2)+1)/2)*(1/2+1/sqrt(2+2*(1/sqrt(1-x^2))))*(1/2+1/sqrt(2+sqrt(2+2*(1/sqrt(1-x^2)))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*(1/sqrt(1-x^2))))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*(1/sqrt(1-x^2)))))))*cdots; abs((1/sqrt(x^2-1))*(1/acoth(x)))=((x/sqrt(x^2-1)+1)/2)*(1/2+1/sqrt(2+2*x*(1/sqrt(x^2-1))))*(1/2+1/sqrt(2+sqrt(2+2*x*(1/sqrt(x^2-1)))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+2*x*(1/sqrt(x^2-1))))))*(1/2+1/sqrt(2+sqrt(2+sqrt(2+sqrt(2+2*x*(1/sqrt(x^2-1)))))))*cdots; have a nice day FME...