" How can I create this?"
Probably using vectorization and/or loops and/or recursion.
"Should I be creating this as a string?"
NO!
If you are able to generate this as a string, then it is also possible to generate it directly as operations on numeric input arguments. Using eval on a string just adds an extra inefficient layer of complexity.
"... is there any simple way?"
Loops and vectorization are simple... recursion a little less so, but still doable.
Could you please clarify a few things:
1- for completeness please provide the output for i=1.
2- mismatching parentheses around the last term of i=3 please confirm:
T(c+(((8*9^0)+(8*9^1) - 2*9^2)))
% ^ missing ?
3- mismatching parentheses around the last term of i=4 please confirm:
T(c+(((8*9^0)+(8*9^1)+(8*9^2) - 2*9^3)))
% ^ missing?
4- You write that the output is "...some matrix variable T_dot ...", but all of the indexing into T appears to be scalar, which means that T_dot would also be scalar. What do you mean that T_dot is a "matrix variable", when your own examples show that it is scalar?
It is an interesting task, if you have some patience I will look at it now...
