EXPINT

Purpose:

Evaluates E_n(z), the generalized exponential integral.

EXPINT(n, z)

n	-	Optional. A scalar or series, the power factor. Defaults to 1.0
z	-	A scalar or series, the exponential factor.

A scalar or series, the value of E_n(z), the integration of exp(-zt) / tⁿ from 1 to ∞.

expint(2)

returns 0.4890 which is identical to expint(1, 2).

expint(3, 0)

returns 0.5.

expint(2, 3 + 2i)

returns -0.00723 - 0.00638i.

W1: expint(1, 1..0.1..1.4)

W1 contains the series {0.21938, 0.18599, 0.15841, 0.13545, 0.11622}.

real(expint(-5..0.01..5));

xlabel("x");ylabel("E_0(x)");label("E_0 Integral");

returns 1001 samples of the real part of E₀(x) with integration limits from -5 to 5.

The generalized exponential integral, E_n(z), is defined as:

where n is the power factor and z is the exponential factor.

For n > 1,

For n = 1,

For real(z) > 0,

where Ci(z) is the Cosine Integral implemented by COSINT and Si(z) is the Sine Integral implemented by SININT.

The closely related Cauchy principal value exponential integral, Ei(z) is defined as:

For real positive z:

and for real negative z:

E_n(0) = ∞