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fresnel cos

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Fresnel cos integral.

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

using namespace Maths::Special;

double fresnel_cos (double x)
Fresnel cos integral.
ExcelReal cc_fresnel_cos (Real x)
This function is available as a Microsoft Excel add-in.

Function Documentation

Fresnel Cos Calculator
  
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doublefresnel_cosdoublex )
Evaluates the cosine Fresnel integral.

(1)
\displaystyle C(x) = \int_0^x cos(\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 S(x) = 0.5 - f(x) cos(\frac{\pi}{2} x^2) - g(x) sin(\frac{\pi}{2} x^2)

Accuracy:
                         Relative error.
  domain     # trials      peak         rms
   0, 10       10000       1.8e-15     3.3e-16
 
Parameters:
xmain 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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