Subject: derivatives of bessel_j A&S 9.1.27 vs 9.1.30
From: Barton Willis
Date: Wed, 24 Jan 2007 10:25:58 -0600
Would it be OK to change the derivatives of the Bessel functions
to use A&S 9.1.27 instead of 9.1.30? See:
http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=200&Page=361
This change allows taylor to expand bessel_j about zero:
(%i1) e : bessel_j(0,x)$
(%i2) taylor(e,x,0,4);
`taylor' encountered an unfamiliar singularity in: bessel_j(0,x)
The cause is
(%i3) diff(e,x,2);
(%o3) bessel_j(1,x)/x-bessel_j(0,x) <--- problem at zero
With the change to A&S 9.1.27:
(%i4) load("c:/maximacvs3/src/bessel.lisp")$
(%i5) taylor(e,x,0,4);
(%o5) 1-x^2/4+x^4/64+...
(%i6) diff(e,x,2);
(%o6) -(bessel_j(0,x)-bessel_j(2,x))/2
With the exception of #10 in rtest14, I think the test suite is OK with
this
change (rtest14 #10 checks diff(bessel_j(1,x),x) =
bessel_j(0,x)-bessel_j(1,x)/x
So it's a non bug failure)
Barton