. This exercise establishes the equality of XXXXXXXXXXand XXXXXXXXXXTo see this, note that XXXXXXXXXXcan be rewritten as Completing the square for the term in parentheses gives Recalling that we...

.
This exercise establishes the equality of (13.6) and (13.7). To see

this, note that (13.6) can be rewritten as

Completing the square for the term in parentheses gives

Recalling that we defined

show that the second summation in the brackets is zero.

.
Establish the identities in (13.12) and (13.13).