# FRESNELC

## Purpose:

Evaluates the Fresnel Cosine Integral.

## Syntax:

FRESNELC(x, xc)

x |
- |
A real or series, the integration limit. |

xc |
- |
Optional. A real, the cutoff limit that determines
the integration limit. Defaults to 1.8. |

## Returns:

A scalar or series, the value of C(x), the integration of cos(*πt*^{2}/2)
from 0 to *x*.

## Example:

fresnelc(1)

returns 0.779893 the value of:

## Example:

fresnelc({0.1, 0.2, 1, 2})

returns {0.099998, 0.199921, 0.779893,
0.488253}, the value of the integral with limits {0.1, 0.2, 1, 2}.

## Example:

fresnelc(-5..0.01..5);

xlabel("x");ylabel("C(x)");label("Cosine
Fresnel");

returns 1001 samples of the Fresnel Cosine Integral with integration
limits from –5 to 5.

## Remarks:

The Fresnel Cosine Integral, C(x), is
defined as:

For abs(**x**)
< **xc**, a power series
about **x**
= 0 is used yielding an
accuracy better than 5e-16.

For abs(**x**)
> **xc**, a minimax rational
approximation based on auxilliary functions described in [1] is used yielding
an accuracy better than 1e-9.

See FRESNELS to evaluate the sine form of
the Fresnel integral.

FRESNELC was developed from an algorithm by J. N. McElwaine.

## See Also:

COSINT

ERF

FRESNELS

GAMMA

GAMMALN

## References:

[1] Abramowitz
and Stegun

*Handbook of Mathematical Functions*
(9th printing 1970)

US
Gov. Printing Office

Section
7.3 p300