Parseval's equality and theorem?

[car202]

It's kind of dumb question..
But, I just wanted to make sure.
Are Parseval's equality and Parseval's theorem same thing? (In terms of Fourier series)
i.e. do both mean \frac{1}{L}\int_c^{c+2L}|f(x)|^{2}dx = \frac{a_0^2}{2}+\sum_{n=1}^{\infty}[|a_n|^{2}+|b_n|^{2}]

 

[HallsofIvy]

Basically, yes. Parceval's equality is the equality you give. Parseval's thereom is the statement that that equality holds, under given hypotheses, of course. Perhaps the crucial difference is the hypotheses. Parceval's equality doesn't make sense without specifying what "f", "a_n", "b_n", etc. are.