Subject: bessel_i value at inf not known by integrate
From: Edwin Woollett
Date: Mon, 31 Oct 2011 14:23:41 -0700
The integral of bessel_i(1,%i*x) over (1,inf)
using integrate returns an error message that
the integral is divergent.
------------------------------
(%i1) display2d:false$
(%i2) integrate(bessel_i(1,%i*x),x,1,inf);
defint: integral is divergent.
-- an error. To debug this try: debugmode(true);
--------------------------------
The indefinite integral is:
---------------------------
(%i3) vx: integrate(bessel_i(1,%i*x),x);
(%o3) %i*bessel_i(0,%i*x)
----------------------------------
The value of the integral comes
entirely from the lower limit:
-----------------------------
(%i4) -float(subst(x=1,vx));
(%o4) -0.76519768655797*%i
-----------------------------------
which is the correct answer for the
integral. The upper limit should be
zero, but:
---------------------------------
(%i5) limit(vx,x,inf,minus);
(%o5) %i*bessel_i(0,infinity)
(%i6) float(%);
(%o6) %i*bessel_i(0.0,infinity)
--------------------------------
Ted Woollett