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[0FH]Give two sequences \((a_{n})_ n\) and \((b_{n})_ n\) to real or complex values, their Cauchy product is the sequence \((c_{n})_ n\) given by
\[ c_{n}{\stackrel{.}{=}}β _{k=0}^{n}a_{k}b_{n-k}\quad . \]
[0FH]Give two sequences \((a_{n})_ n\) and \((b_{n})_ n\) to real or complex values, their Cauchy product is the sequence \((c_{n})_ n\) given by