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Taylor polynomials of Bessel functions #1220

Closed rtoy closed 4 months ago

rtoy commented 4 months ago

Imported from SourceForge on 2024-07-04 06:49:38 Created by willisbl on 2007-01-22 10:36:11 Original: https://sourceforge.net/p/maxima/bugs/1082

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.

rtoy commented 4 months ago

Imported from SourceForge on 2024-07-04 06:49:39 Created by willisbl on 2007-01-28 20:16:41 Original: https://sourceforge.net/p/maxima/bugs/1082/#9bdc

rtoy commented 4 months ago

Imported from SourceForge on 2024-07-04 06:49:42 Created by willisbl on 2007-01-28 20:16:41 Original: https://sourceforge.net/p/maxima/bugs/1082/#24be

Logged In: YES user_id=895922 Originator: YES

Fixed in bessel.lisp CVS r 1.39