Exchange of product and sum

All products added together are multiplied by the sum

• $\sum_{i,j} a_i \times b_j = (\sum_i a_i) \times (\sum_j b_j)$ It looks like a special law, but it just uses a lot of distributive law.
• Distribution law: $a \times b + a \times c = a \times (b + c)$

More use formal power series (corresponding to an infinite sequence of numbers) for infinite sums

• $\sum_i^\infty x^{ai} \times \sum_j^\infty x^{bj} = \sum_i^\infty\sum_j^\infty x^{ai+bj}$

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