At its core, mine is a very simple communication error between me and Mathematica that I haven't been able to crack, so I do apologise if it seems embarassingly inane.
Please consider the following simplified set-up. I have x[-1] and I seek an expression for x[5] using Table:
root = Table[Solve[2x[b]+x[b-1]+b == 0, x[b]] /.x[-1]->1, {b,0,5}]
The output:
{{{x[0]->-(1/2)}}, {{x[1] -> 1/2 (-1 - x[0])}}, {{x[2] -> 1/2 (-2 - x[1])}},
{{x[3] -> 1/2 (-3 - x[2])}}, {{x[4] -> 1/2 (-4 - x[3])}},
{{x[5] -> 1/2 (-5 - x[4])}}}.
(I don't have the right lingo for this, but) the output elements don't engage like numbers. If I were to try something like root[[1]]+1,
I would get
{{1 + (x[0] -> -(1/2))}}
(and Rules->Equal just changes that -> to =; the behaviour remains the same).
Is it possible to define these x[b] such that back-substitution happens while Table is at work? If not, can you please advise on how to define individual output elements (without directly assigning values from the output to each x[b])?
As an aside, is it better Mathematica practice to abandon this whole Table business and use a loop instead?
So many thanks in advance!
--PhysicsHobbit
