1. Approssimazioni numeriche / Numerical approximations

Pi = 3.1415926535... approx -1/2+(11/7) Log[2] Exp[(Log[3])^2] Absolute Error <1.31 E-7

Feig1=4.669201609... approx 2/(Pi*(Log[2]^(2*E)))=4.669201717... | Rel. err. | < 2.4 E-8

Pi= 3.1415926535... approx 3*Exp(1/3)/(4*EulerGamma^2)=3.1415926567... | Rel. err. | < 1 E-9

Sum[((-1)^i)/((Log[i])^4),[i,2,40000]] approximated 3.82453

Sum[((-1)^i)/((Log[i])^10),[i,2,10000]] approximated 38.702384240321707

Alessandro Soranzo (2013)

2. Il grafico di f(x)=exp(1/log x) e' simmetrico rispetto alla bisettrice del I quadrante. The graph of f(x)=exp(1/log x) is symmetric with respect to the bisecting line of the I quadrant

(Infatti la funzione coincide con la sua inversa perche' f(f(x))=x). (Because the function is equal to its inverse because f(f(x))=x). (Si noti che la funzione non e' ne' crescente ne' decrescente sul dominio). (Notice that the function is neither increasing nor decreasing on its domain).

Alessandro Soranzo (2015)