Some bessel limits that would be nice to not get an error or a noun form.
assuming(a>0);
limit(bessel_i(a, x)/(1/sqrt(2 * %pi * x) * exp(x)), x, inf);
-> 1
limit(bessel_k(a, x)/(sqrt(%pi / (2 * x)) * exp(-x)), x, inf);
-> 1
limit(bessel_j(a, x)/(sqrt(2/(%pi*x))*cos(x - a*%pi/2 - %pi/4)), x, inf);
-> 1
limit(bessel_y(a, x)/(sqrt(2/(%pi*x))*sin(x - a*%pi/2 - %pi/4)), x, inf);
-> 1
These can all be obtained from this Wikipedia site plus more.
http://en.wikipedia.org/wiki/Bessel_function
Rich
------------Original Message------------
From: "Richard Hennessy"<rvh2007 at comcast.net>
To: "Maxima List" <maxima at math.utexas.edu>
Date: Sat, Jul-5-2008 8:16 AM
Subject: Bessel Asymptotic forms do not work
(%i1) besselexpand:true$
(%i2)limit(bessel_k(1/6,x)/(sqrt(Pi/(2*x)) * exp(-x)) ,x,inf)
(%o2)(sqrt(2)*(limit(bessel_k(1/6,x)*sqrt(x)*%e^x,x,inf)))/sqrt(Pi)
which I think should be 1.
so
(%i3) limit(bessel_k(1/6,x)/(sqrt(Pi/(2*x)) * exp(-x)) ,x,inf)
(%o3) 1
would be much nicer.
Rich
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