05/25/2015, 11:29 PM

I noticed a possible pattern.

next

next

define :

then

Now it appears

The continuum sum up to z-1 of exp^[n](x) is given by

CS [ exp^[n](x) , z-1] = P_n(x) + F_n(x)

where F_n is 2pi i periodic and P_n is a polynomial of degree (at most) n.

I guess there is a simple reason for it.

Right ??

What if n is not an integer ? say n = 3/2 ?

Does that imply P_{3/2}(x) =< O( x^{3/2} ) ??

regards

tommy1729

next

next

define :

then

Now it appears

The continuum sum up to z-1 of exp^[n](x) is given by

CS [ exp^[n](x) , z-1] = P_n(x) + F_n(x)

where F_n is 2pi i periodic and P_n is a polynomial of degree (at most) n.

I guess there is a simple reason for it.

Right ??

What if n is not an integer ? say n = 3/2 ?

Does that imply P_{3/2}(x) =< O( x^{3/2} ) ??

regards

tommy1729