CodeCogs

Fresnel sin integral.

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Interface

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

using namespace Maths::Special;

Evaluates the sine Fresnel integral

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

(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)

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

main input argument

Interactive Calculator

Result –