How to compute (numerically)

$$ F(x) = \int_{-\infty}^x \dfrac{\sin(t)}{t} dt $$

  • 2
    $\begingroup$ Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc. $\endgroup$
    – KingLogic
    Commented Jan 20, 2021 at 3:53
  • $\begingroup$ @KingLogic $F(x)$ is the source function for the PDE that I am solving (numerically). I just need to compute $F(x)$ to solve the PDE (that is part of wave propagation simulation code). $\endgroup$ Commented Jan 20, 2021 at 3:58
  • $\begingroup$ Start by breaking up the integral into the regions $(-\infty, 0)$ and $(0, x)$, then over $(x, \infty)$. $\endgroup$ Commented Jan 20, 2021 at 3:59
  • $\begingroup$ Consider the Taylor series of $\sin t$ $\endgroup$
    – PM 2Ring
    Commented Jan 20, 2021 at 4:08

1 Answer 1


$$F(x) = \int_{-\infty}^x \dfrac{\sin(t)}{t} dt=\text{Si}(x)+\frac{\pi }{2}$$

For the computation of the sine integral function, you will find subroutines in Numerical Recipes (have a look here).


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