Re: Integration Methods in PARI

[kevin lucas <lucaskevin296@gmail.com>]

I made a mistake copying the integral from paper, it should have been

intnum(x=0, +oo, x*exp(cos(x))*sin(sin(x))/(x^2+1))

Any help or references, PARI-specific or otherwise, for integrating such oscillating integrals are welcome. I apologize for the mistake.

On Fri, Mar 16, 2018 at 8:09 PM, kevin lucas <lucaskevin296@gmail.com> wrote:

I made a mistake copying the integral from paper, it should have been

intnum(x=0, +oo, x*exp(cos(x))*sin(sin(x))/(x^2+1))

Any help or references, PARI-specific or otherwise, for integrating such oscillating integrals are welcome. I apologize for the mistake.

On Fri, Mar 16, 2018 at 5:57 PM, <Henri.Cohen@math.u-bordeaux.fr> wrote:

Quoting kevin lucas <lucaskevin296@gmail.com>:

I have been trying to evaluate the following integral in PARI:

intnum(x=0, +oo, x*exp(cos(x))*sin(sin(x))/(x^2-1))

As Bill says, the error is due to the fact that your integral diverges at
x=1. But even once this is repaired, Pari is unable to integrate an
oscillating function of this type; in fact I would be surprised if
any software could do it. And Bill's suggestion of finding the Fourier
expansion will very probably not work.