Parseval's Identity Application

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In this video, it is stated that Parseval's Identity "is how we go from discrete to continuous." However, I have not been able to find any material that expands on this use of Parseval's Identity. I have discovered that it is the inner product version of the Pythagorean Theorem.

What does this quote that Parseval's Identity "is how we go from discrete to continuous" mean? Is Parseval's Identity a bridge between recurrence relations and differential equations somehow? In this vein, is it related to time-scale calculus or this application of generating functions?

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