Table 8.2.13(a) lists , the first six members of the Cauchy product. From the listing in the table, generalize that if , then for each , the first and last members are zero, and the terms of the Cauchy product reduce to the pattern shown in Table 8.2.13(b).
|
|
Table 8.2.13(a) Terms of the Cauchy product
|
Table 8.2.13(b) Cauchy product when
|
|
|
In practice, it appears to be easier to define and to be zero, and to use the existing definition of .