Say if I define a power series over some arbitrary field $F$ as
$$a = \sum^{ \infty }_{i = 0} a_{i} X^{i} $$
Then can I say:
$$ab = \sum^{ \infty }_{i = 0} \sum^{ \infty }_{j = 0} a_{i} b_{j} X^{i + j} $$
Say if I define a power series over some arbitrary field $F$ as
$$a = \sum^{ \infty }_{i = 0} a_{i} X^{i} $$
Then can I say:
$$ab = \sum^{ \infty }_{i = 0} \sum^{ \infty }_{j = 0} a_{i} b_{j} X^{i + j} $$