I'm having trouble interpreting the following result of RSolve
to this difference equation:
RSolve[n1 F[n1+1, n2] == (n1+n2) F[n1, n2] + F[n1-1, n2+1] - F[n1, n2+1],
F[n1, n2], n1]
The result makes no sense to me, since it is expressed as a sum over K[1]
starting at K[1] = 0
causing the factorial (-1 + K[1])!
to diverge.
Is there some special interpretation of this factorial?
F
on the right-hand-side, so it's not really a solution. In any case, your recurrence relation does not really defineF
for alln1,n2
, so it cannot really be solved. Not sure how to interpret the output by MMA though. $\endgroup$ – AccidentalFourierTransform May 6 '18 at 21:46