EXPINT

Purpose:

Evaluates En(z), the generalized exponential integral.

Syntax:

EXPINT(n, z)

n

-

Optional. A scalar or series, the power factor. Defaults to 1.0

z

-

A scalar or series, the exponential factor.

Returns:

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

Example:

expint(2)

 

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

Example:

expint(3, 0)

 

returns 0.5.

Example:

expint(2, 3 + 2i)

 

returns -0.00723 - 0.00638i.

Example:

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

 

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

Example:

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.

Remarks:

The generalized exponential integral,  En(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:

 

 

See EXPINTEI to evaluate the Cauchy principal value exponential integral.

 

En(z) is real for real n and real positive z.

 

En(0) =

See Also:

BETAINC

COSINT

EXPINTEI

GAMMA

GAMMAINC

SININT