(just some curiosities about this type of series)
i will use
for the difference operator
and if and only if (the indefinite summation)
we have the summation by parts method
(its similar to the integration by parts)
if we apply this method "n" times we get
[tex]\sum\limits_{x} g(x).\Delta f(x)=[/tex]
( where )
if, g(x) has degree n , (so )and we can use it on the summation by parts to find
where
if and e c=0
but (here it's the stirling number of the second kind, knuth's notation )
so