Originally Posted by Havelock
here should be
be any non-negative number. Consider the integral
Develop into a geometrical series and perform the double integration. Then we obtain
put this in (1) and integrate the sum term by term to get (2).
if we put we'll get: where now since and
. Then we can write this sum as
If we put then assertion a) follows immediately.
we have also since we have thus
If we differentiate with respect to
, then integral (1) changes into
and summation (2) becomes
and assertion (b) now follows straight away.
exactly the same argument as above but this time and thus the denominator will divide