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When attemtpting to find the Cauchy product of two functs f(x) and g(x), which are themselves power series, is it more important to have their respective terms of summation be the same of for the exponent of their respective x variable to be equal? Or must both of these conditions be met? I am in a situation where it seems that shifting the index for f(x) to make x powers equal, makes the initial summation counters not equal. Not sure which of these conditions is needed to apply Cauchy prod theorem.