Method on @sym: fresnels (x) ¶

Symbolic Fresnel Sine function.

The Fresnel Sine function can be created with:

syms x
z = fresnels (x)
  ⇒ z = (sym) S(x)

There are different definitions in the literative involving antiderivative of sin(x^2). Here we have the normalized Fresnel Sine integral where:

diff (z)
  ⇒ (sym)
         ⎛   2⎞
         ⎜π⋅x ⎟
      sin⎜────⎟
         ⎝ 2  ⎠

Specifically, the (normalized) Fresnel Sine function is given by the integral:

rewrite (z, 'Integral')
  ⇒ (sym)
      x
      ⌠
      ⎮    ⎛ 2  ⎞
      ⎮    ⎜t ⋅π⎟
      ⎮ sin⎜────⎟ dt
      ⎮    ⎝ 2  ⎠
      ⌡
      0

See also: @@sym/fresnelc.

Package: symbolic