Method on @sym: sinint (x) ¶

Symbolic sine integral function.

The sine integral function can be created with:

syms x
y = sinint (x)
  ⇒ y = (sym) Si(x)

It is an antiderivative of sin(x)/x:

diff (y, x)
  ⇒ (sym)
      sin(x)
      ──────
        x

Specifically, the sine integral function is:

syms t
int (sin (t)/t, t, 0, x)
  ⇒ (sym) Si(x)

This can instead be written in terms of the sinc function (see ‘@sym/sinc’) where:

rewrite (y, 'Integral')
  ⇒ (sym)
      x
      ⌠
      ⎮     ⎛t⎞
      ⎮ sinc⎜─⎟ dt
      ⎮     ⎝π⎠
      ⌡
      0

See also: @sym/cosint, @sym/sinc.

Package: symbolic