This expression leaves us however with some terms with negative indices, for example x(−1) and x(−2) which may not be defined. Our vector x has components x(0), x(1), x(2) and x(3).
The index j for x runs from j=0 to j=3 since x is meant to represent a third-order polynomial.
Furthermore, the index i runs from i=0 to i=5 since y contains the coefficients of a fifth-order polynomial. When i=5 we may also have values of x(4) and x(5) which are not defined.