Subject: Why cannot Maxima calculate some simple sums
From: andre maute
Date: Wed, 23 Dec 2009 14:48:45 +0100
On Wednesday 23 December 2009, ??? wrote:
> I find Maxima interesting and useful ,but it seems that its infinite sum
> function is broken.
> When I type sum(1/k^2,k,1,inf),simpsum and enter ,it gives the correct
> answer %pi^2/6
> But when I type sum(1/k!,k,1,inf),simpsum and enter,it does nothing ,just
> to return the expression,which is ridiculous since that series simply
> converges to %e
> And it cannot calculate even 1/(k(k+1))
> Is this a bug ,an unimplemented feature or I missed something necessary to
> calculate infinite series?
use the simplify_sum package
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~$ maxima -b simpsum1.max
Maxima 5.19.1 http://maxima.sourceforge.net
Using Lisp SBCL 1.0.18.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(simpsum1.max)
batching /home/user/simpsum1.max
(%i2) display2d : false
(%o2) false
(%i3) load("simplify_sum")
(%i4) h:sum(1/k^2,k,1,inf)
(%o4) 'sum(1/k^2,k,1,inf)
(%i5) simplify_sum(h)
(%o5) %pi^2/6
(%i6) h:sum(1/(k*(1+k)),k,1,inf)
(%o6) 'sum(1/(k*(k+1)),k,1,inf)
(%i7) simplify_sum(h)
(%o7) 1
(%i8) h:sum(1/k!,k,0,inf)
(%o8) 'sum(1/k!,k,0,inf)
(%i9) simplify_sum(h)
(%o9) %e
(%i10) h:sum(1/k!,k,1,inf)
(%o10) 'sum(1/k!,k,1,inf)
(%i11) simplify_sum(h)
(%o11) sqrt(%e)*sqrt(%pi)*bessel_i(1/2,1/2)
(%o11) "/home/user/simpsum1.max"
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