fresnel_cos — Special

Fresnel cos integral.

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Interface

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

using namespace Maths::Special;

Evaluates the cosine Fresnel integral.

$$C(x) = \int_0^x cos(\frac{\pi}{2} t^2) dt$$

(1)

\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

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

(2)

<pre> Relative error. domain # trials peak rms 0, 10 10000 1.8e-15 3.3e-16 </pre>

main input argument

Interactive Calculator

Result –