## Cauchy Product Definition

Cauchy Product:
The Cauchy product of two infinite series is defined by $\displaystyle (\sum_{i=0}^\infty a_i)\cdot(\sum_{j=0}^\infty b_j)=\sum_{k=0}^\infty c_k$ where $c_k=\sum_{l=0}^k a_lb_{k-l}$.