SININT

Purpose:

Evaluates Si(z), the Sine Integral.

Syntax:

SININT(z)

z

-

A scalar or series, the integration limit.

Returns:

A scalar or series, the value of Si(z), the integration of sin(t) / t from 0 to z.

Example:

sinint(1)

 

returns 0.946083 the value of:

 

 

Example:

sinint(1 + i)

 

returns 1.104223 + 0.882454i.

Example:

sinint(-10..0.01..10);

xlabel("x");ylabel("Si(x)");label("Sine Integral");

 

returns 2001 samples of Si(x) with integration limits from -10 to 10.

Example:

W1: 0.01..0.01..10

W2: sinint(W1)

W3: integ(sin(w1) / w1)

 

W2 contains the sine integral and W3 computes an approximation by directly integrating sin(t) / t.

Remarks:

The Sine Integral, Si(z), is defined as:

 

 

The input z may be complex.

 

 

for real(z) > 0 and Ei(z) is the Cauchy principal value exponential integral implemented by EXPINTEI.

 

See COSINT to evaluate the Cosine Integral.

See Also:

COSINT

EXPINT

EXPINTEI

FRESNELC

FRESNELS