02/14/2015, 12:36 AM

W.J. Thron, Sequences generated by iteration., Trans. Am. Math. Soc. 96 (1960), 38-53

(English).

This is relevant.

W.J Thron proves that the integral can be truncated to A x^B under some conditions that come from this theorem :

(Thron 1960 Theorem 3.1.). Let f be analytic at 0 with powerseries expansion of the following form :

f(x) = x - a_m x^m + a_(m+1) x^(m+1) + ...

with a_m < 0.

then lim n -> oo

n^(1/(m-1)) h^[n](x) = (- a_m(m - 1))^(1/(m-1))

From which it follows.

regards

tommy1729

(English).

This is relevant.

W.J Thron proves that the integral can be truncated to A x^B under some conditions that come from this theorem :

(Thron 1960 Theorem 3.1.). Let f be analytic at 0 with powerseries expansion of the following form :

f(x) = x - a_m x^m + a_(m+1) x^(m+1) + ...

with a_m < 0.

then lim n -> oo

n^(1/(m-1)) h^[n](x) = (- a_m(m - 1))^(1/(m-1))

From which it follows.

regards

tommy1729