Method on @sym: fresnelc (x) ¶

Symbolic Fresnel Cosine function.

The Fresnel Cosine function can be created with:

syms x
z = fresnelc (x)
  ⇒ z = (sym) C(x)

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

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

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

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

See also: @@sym/fresnels.

Package: symbolic