fresnel sin

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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.

Fresnel Sin Calculator

doublefresnel_sin( double x )

Evaluates the sine Fresnel integral

(1)

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

$\graph x=-4:4$

The integral is evaluated by a power series for x < 1.

For x >= 1 auxiliary functions f(x) and g(x) are employed such that

(2)

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

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

x	main input argument

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

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Last Modified: 18 Oct 07 @ 17:07 Page Rendered: 2009-01-05 22:49:37