[Maxima] solve_rec problem
eric.reyssat at math.unicaen.fr
Tue Jun 9 15:07:55 CDT 2009
Richard Hennessy a écrit :
> I think I don't understand solve_rec() in the solve_rec package.
> I tried
> (%i13) display2d:false;
> (out13) false
> (%i14) solve_rec(a[i]=x*a[i-1]/(6*i*(6*i+1)),a[i]);
> (out14) a[i] = gamma(1/6)*%k*6^(1-2*i)*x^i/(6*i!*gamma(i+7/6))
> (%i15) solve_rec(a[i]=x*a[i-6]/(i*(i+1)),a[i]);
> (out15) false
> Should the answer in the second case not be false, I have the
> recurrence relation which skips over 5 terms so a[i] = f(a[i-6]) but
> why do I have to rewrite it so a[i]=f(a[i-1])?
in principle, you may skip terms in a recurrence relation if you wish.
This just makes the result more complex, possibly not expressible in
terms of usual functions.
For instance the so-called double factorial (see
http://en.wikipedia.org/wiki/Factorial#Double_factorial) defined by
f(n)=1 for n<2 and f(n)=n.f(n-2) for n>1 is not solved :
But the simpler recurrence f(n)=2.f(n-2) , which also skips one term, is
(%o4) a[i] = %k*2^(i/2)*(-1)^i+%k*2^(i/2)
and also f(n)=2.f(n-6) :
(%o5) a[i] = %k*2^(i/6)*(-1)^i+%k*2^(i/6)
Your second case seems to be just too complex to be solved (and
definitely doesn't represent the same sequence as your first case !).
Hope this helps.
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