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RSolve capabilities


$VersionNumber
5.2

No questions here.
Just an example of Mathematica's
capabilities.
I don't believe that the following recurence relation
is something trivial!

In[8]:=
sys = {F[n + 2] == n*F[n + 1] + F[n], F[0] == 0, F[1] == 1};

In[10]:=
FullSimplify[RSolve[sys, F[n], n]]

Out[10]=
{{F[n] -> 2*(BesselI[-1 + n, -2]*BesselK[1, 2] + BesselI[1,
2]*BesselK[-1 + n, 2])}}

In[11]:=
F[n_] = %[[1,1,2]];

In[15]:=
Off[N::meprec]
FullSimplify[sys]
On[N::meprec]

Out[15]=
{True, True, True}

Nice job!

Dimitris



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