quad_qag and quad_qags fail with imagpart( bessel_i(1, %i*x)) arg
Subject: quad_qag and quad_qags fail with imagpart( bessel_i(1, %i*x)) arg
From: Edwin Woollett
Date: Sat, 22 Oct 2011 14:20:07 -0700
For cases where integrate, numer fails, I am using
either quad_qag or quad_qags for numerical integration
in one dimension.
I automatically split up any integrand into real and
imaginary parts using realpart and imagpart, and
later combine the answers.
This has worked with bessel functions ok up to
my testing of bessel_i(1,%i*x).
(%i4) imagpart(bessel_i(1,%i)),numer;
(%o4) 0.44005058574493
(%i6) quad_qag(imagpart(bessel_i(1,%i*x)),x,1,3,3,limit=700);
(%o6) quad_qag(bessel_i(1,%i*x),x,1,3,3,epsrel = 1.0E-8,epsabs = 0.0,
limit = 700)
(%i11) quad_qags(imagpart(bessel_i(1,%i*x)),x,1,3,limit=700);
(%o11) quad_qags(bessel_i(1,%i*x),x,1,3,epsrel = 1.0E-8,epsabs = 0.0,
limit = 700)
Since imagpart(bessel_i(1,%i*x)) is a real number, why can't
quad_qag and quad_qags cope?
Ted Woollett