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Maths › Special ›

fresnel sin

Fresnel sin integral.

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Contents

Interface
Fresnel Sin
Page Comments

Dependents

Interface

C++

Excel

Fresnel Sin

doublefresnel_sin( double x )

Evaluates the sine Fresnel integral

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

Graph is not currently available

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

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

Accuracy:

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

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

$gennarakis\′s Photo$

26 Nov 10, 5:44AM

how can i add this code to excel so i can compute the fresnel integrals for multiple values?

$Rupert Rawnsley\′s Photo$

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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