About the Project
6 Exponential, Logarithmic, Sine, and Cosine IntegralsProperties

§6.5 Further Interrelations

When x>0,

6.5.1 E1(x±i0)=Ei(x)iπ,
6.5.2 Ei(x)=12(E1(x+i0)+E1(xi0)),
6.5.3 12(Ei(x)+E1(x))=Shi(x)=iSi(ix),
6.5.4 12(Ei(x)E1(x))=Chi(x)=Ci(ix)12πi.

When |phz|<12π,

6.5.5 Si(z) =12i(E1(iz)E1(iz))+12π,
6.5.6 Ci(z) =12(E1(iz)+E1(iz)),
6.5.7 g(z)±if(z)=E1(iz)eiz.