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Very useful fact

02/10/2011

Very useful!
Discrete, sum:
\left[\sum_{i=1}^n a_i\right]\left[\sum_{i=1}^n b_i\right]=\sum_{i=1}^n \sum_{j=1}^n a_ib_j

Continuous, integration:
\left[\int_{t_0}^{t_1} f(\alpha)d\alpha\right]\left[\int_{t_0}^{t_1} g(\alpha)d\alpha\right]=\int_{t_0}^{t_1} \int_{t_0}^{t_1} f(\alpha)g(\beta)d\alpha d\beta

The sum and integration are very similar to each other.

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