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
