[Maxima-bugs] [ maxima-Bugs-1641457 ] Taylor polynomials of Bessel functions

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Bugs item #1641457, was opened at 2007-01-22 04:36
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Category: Lisp Core - Taylor
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: Taylor polynomials of Bessel functions

Initial Comment:
Bessel_j(0,x) is analytic at 0 yet

(%i1) taylor(bessel_j(0,x),x,0,2);
`taylor' encountered an unfamiliar singularity in:

Taylor has no problem expanding bessel_j at 1:

(%i2) taylor(bessel_j(0,x),x,1,2);
(%o2) < junk deleted>

I think the problem with the expansion at zero is
the derivative of bessel_j(0,x) is

(%i3) diff(bessel_j(0,x),x,2);
(%o3) bessel_j(1,x)/x-bessel_j(0,x)

Trying to evaluate this at zero causes problems.

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