# COSINT

## Purpose:

Evaluates Ci(z), the Cosine Integral.

## Syntax:

COSINT(z)

 z - A scalar or series, the integration limit.

## Returns:

A scalar or series, the value of Ci(z), the integration of -cos(t) / t from z to .

## Example:

cosint(1)

returns 0.337404 the value of:

## Example:

cosint(1 + i)

returns 0.882172 + 0.287249i.

## Example:

cosint(0..0.01..10);

xlabel("x");ylabel("Ci(x)");label("Cosine Integral");

returns 1001 samples of Ci(x) with integration limits from 0 to 10.

## Example:

W1: 0.01..0.01..10

W2: cosint(W1)

W3: gamm + ln(w1) + integ((cos(w1) - 1) / w1)

W2 contains the cosine integral and W3 computes an approximation by directly integrating (cos(t) - 1) / t.

## Remarks:

The Cosine Integral, Ci(z), is defined as:

The input z may be complex.

The function can also be computed as:

where γ is the Euler constant implemented by GAMM.

for real(z) > 0 and E1(z) is the generalized exponential integral implemented by EXPINT.

See SININT to evaluate the Sine Integral.