Subject: [Maxima} bessel function simplification tools?
From: Edwin Woollett
Date: Fri, 29 May 2009 15:23:17 -0700
On May 29, Edwin Woollett wrote:
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I would like to show that this explicit function of x
is a solution to the original differential equation by
using the first and second derivatives, but when
expanded I am left with eighteen terms which don't
simplify. (besselexpand:true only helps for orders n/2 with
n odd )
To be able to use Maxima to solve differential equations whose
solutions can be expressed in terms of bessel functions,
we need more simplification tools which know about
bessel functions.
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In fact contrib_ode has ode_check which does this check:
(%i1) display2d:false$
(%i2) de : 'diff(y,x,2) + 'diff(y,x) + x*y;
(%o2) 'diff(y,x,2)+'diff(y,x,1)+x*y
(%i3) load(contrib_ode)$
(%i4) gsoln : contrib_ode(de,y,x);
(%o4) [y = bessel_y(1/3,(4*x-1)^(3/2)/12)*%k2*sqrt(4*x-1)*%e^-(x/2)
+bessel_j(1/3,(4*x-1)^(3/2)/12)*%k1*sqrt(4*x-1)*%e^-(x/2)]
(%i5) ode_check(de,first(gsoln));
(%o5) 0
Sorry for noise,
Ted Woollett