Re: References for Numerical Integration

[Alasdair McAndrew <amca01@gmail.com>]

Check out tanh-sinh quadrature: it is designed for high-precision quadrature of smooth functions.  It is also not too hard to program, if you have arbitrary precision real arithmetic (which you do in Pari/GP).

cheers,

Alasdair

On Mon, Oct 22, 2018 at 4:35 AM kevin lucas <lucaskevin296@gmail.com> wrote:

PARI obviously has some very powerful tools for numerical integration. I have, however, keenly felt the absence of a text treating this area in more detail than the manual. I was recently trying to compute

intnum(x=0,oo, (sin(x)^4)/(x)^2)

I only get about 3 digits (the integral evaluates to log(2)). There's probably a neat way to get more digits in this particular instance. What I'm looking for is a reasonably complete account of such methods, for even more complicated integrals in PARI. I have, for instance met the integral

intnum(x=0,oo, exp(x)*besselj(0,x))

which doesn't even return an answer. Where can I learn how to evaluate such integrals in GP?

References outside just numerical integration are also welcome.

Thanks,

Kevin

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