Subject: Howto simplify Integral with jacobi polynomials
From: andre maute
Date: Thu, 10 Jul 2008 17:00:45 +0200
In order to get the corresponding
weighted L2-norm for the Jacobi polynomials
I tried the following
-------------------------------------------------------------------
~$ maxima -b jacobibug.max
Maxima 5.15.0 http://maxima.sourceforge.net
Using Lisp SBCL 1.0.11.debian
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) batch(jacobibug.max)
batching /home/myuser/jacobibug.max
(%i2) display2d : false
(%o2) false
(%i3) load("orthopoly")
(%o3) "/home/seirios/opt/maxima/share/maxima/5.15.0/share/orthopoly/orthopoly.lisp"
(%i4) declare(k,integer)
(%o4) done
(%i5) assume(k >= 0)
(%o5) [k >= 0]
(%i6) declare(l,integer)
(%o6) done
(%i7) assume(l >= 0)
(%o7) [l >= 0]
(%i8) declare(a,real)
(%o8) done
(%i9) assume(a > -1)
(%o9) [a > -1]
(%i10) declare(b,real)
(%o10) done
(%i11) assume(b > -1)
(%o11) [b > -1]
(%i12) integrate(jacobi_p(k,a,b,x)*jacobi_p(k,a,b,x)*(1-x)^a*(x+1)^b,x,-1,1)
(%o12) pochhammer(a+1,k)^2*('integrate(('sum(
pochhammer(-k,i)*pochhammer(k+b+a+1,i)
*pochhammer(a+1,i)^-1
*i!^-1*((1-x)/2)^i,i,
0,k))
^2
*(1-x)^a*(x+1)^b,x,-1,1))
/k!^2
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Do i have to write my own simplification rule?
For the documentation, especially the orthopoly section,
Abramowitz & Stegun (A&S) is freely available
but Gradshteyn & Ryzhik and Merzbacher are not.
Couldn't the documentation be a litlle bit more specific
at least for the nonfree citations?
Perhaps implementing the tables of A&S would help here also.
Andre