- #1
hholzer
- 37
- 0
If a_0 + (a_1)x + (a_2)x^2 + ...
and
b_0 + (b_1)x + (b_2)x^2 + ...
are two power series and the coefficient
of x^r from their product is a power series:
(a_0)(b_r) + (a_1)(b_(r-1)) + ...
What principle or theorem or definition(s)
are we applying when finding that this is
indeed the coefficient of the x^r term of
the product of two power series?
and
b_0 + (b_1)x + (b_2)x^2 + ...
are two power series and the coefficient
of x^r from their product is a power series:
(a_0)(b_r) + (a_1)(b_(r-1)) + ...
What principle or theorem or definition(s)
are we applying when finding that this is
indeed the coefficient of the x^r term of
the product of two power series?