Digital Library of Mathematical Functions
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6 Exponential, Logarithmic, Sine, and Cosine IntegralsProperties

§6.5 Further Interrelations

When x>0,

6.5.1 E1(-x±0)=-Ei(x)π,
6.5.2 Ei(x)=-12(E1(-x+0)+E1(-x-0)),
6.5.3 12(Ei(x)+E1(x))=Shi(x)=-Si(x),
6.5.4 12(Ei(x)-E1(x))=Chi(x)=Ci(x)-12π.

When |phz|<12π,

6.5.5 Si(z) =12(E1(-z)-E1(z))+12π,
6.5.6 Ci(z) =-12(E1(z)+E1(-z)),
6.5.7 g(z)±f(z)=E1(z)z.