From bug-octave-request at bevo dot che dot wisc dot edu  Thu Feb 19 11:09:28 1998
Subject: besselj bug  at cygwin32
From: fabian at olymp dot Umwelt dot TU-Cottbus dot de (Rolf Fabian)
To: bug-octave at bevo dot che dot wisc dot edu
Date: Thu, 19 Feb 1998 18:10:03 +0100

Dear John W.,


BUG-REPORT for platform
cygwin32-octave2.0.10-binary downloaded 980217 from your server)

   besselj(N,x) - function, now implemented in 2.0.10
   produces OVERALL GARBAGE even for the most simple 'besselj(0,x)'
   e.g.:
   TEST 1:
   octave:> besselj(N=0, x0=2.406)
   ans=-0.44721
	this is complete nonsense, because x0 is approx. the first zero of J(0,x)

   TEST 2:
   octave:> besselj(N=1, xm=5.1)
   ans=-5.7407
	this is complete nonsense, because xm is approx. the global minimum of J(1,x)
        with a value of about J(1,xm)=-0.3

   TEST 3: higher order N test:
   octave:> bessel(N=8, x=10)
   ans = -17.223
   -  nonsense: As seen from the asymptotic behaviour of J(N,x) for large x->inf
     	J(N,x) -> sqrt( (2/pi)/x ) * ( cos (x -pi*N/2 -pi/4) ) 
     all the J-functions approach asymptotically the x-axis and their
     abs-value can never be larger than
		 sqrt( (2/pi)/x )
     which is *always* smaller than 1, if x>1, independant from N


Best wishes
Rolf Fabian fabian at umwelt dot tu-cottbus dot de 980219