SpecialFuncs.EI Method

function EI(X: Double): Double;

Exponential integral Ei(x).

#NameDescription
1XArgument of the exponential integral
2must not be zero.

Returns: Double - the exponential integral Ei(x).

Remarks:

Computes the exponential integral, the Cauchy principal value of

Ei(x)=-integral _(-x)^(inf)(e^(-t))/t dt=p.v.integral _(-inf)^xe^t/t dt.

Domain: any real x \ne 0 (Ei has a logarithmic singularity at the origin). It is related to the complementary integral by Ei(x) = -E1(-x) for x > 0. Ei(x)<0 for x<0, crosses zero near x \approx 0.3725, and grows like e^{x}/x for large positive x.

See Also: SpecialFuncs.E1, SpecialFuncs.ExpEI