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fresnel sin

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Fresnel sin integral.

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Contents

Interface
Function Documentation
Page Comments

Interface

#include <codecogs/maths/special/fresnel_sin.h>

using namespace Maths::Special;

	double	`fresnel_sin` (double x) Fresnel sin integral.
	Real	cc_fresnel_sin (Real x) This function is available as a Microsoft Excel add-in.

Function Documentation

Fresnel Sin Calculator

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doublefresnel_sin( double x )

Evaluates the sine Fresnel integral

(1)

$S(x) = \int_0^x sin(\frac{\pi}{2} t^2) dt$

$\graph x=-4:4$

The integral is evaluated by a power series for x < 1. \n \n For x >= 1 auxiliary functions f(x) and g(x) are employed such that

(2)

$C(x) = 0.5 + f(x) sin(\frac{\pi}{2} x^2) - g(x) cos(\frac{\pi}{2} x^2)$

Accuracy:

                       Relative error.
 domain     # trials      peak         rms
  0, 10       10000       2.0e-15     3.2e-16

Parameters:

x	main input argument

Authors:

Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
Documentation Nick Owens

Source Code:

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Page Comments

$Rupert Rawnsley\′s Photo$

Rupert Rawnsley

3 Jun 09, 3:41PM

Implementation error

I think the sign for this function may be inverted. Compare the graph with the wiki page: http://en.wikipedia.org/wiki/Fresnel_integral

In the code, the sign variable is being calculated incorrectly. Replacing

int sign = 2*(x<0) - 1;

with something like

const int sign = x > 0 ? +1 : -1;

should fix it.

The same thing applies to the cosine equivalent.

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Last Modified: 18 Oct 07 @ 17:07 Page Rendered: 2010-03-12 11:45:40