Question

if \(f(x) = O(x^r)\) as \( x \rightarrow \infty \), show that \[\int_0^{f(x)}{e^{-u}(1+\frac{u}{x})^x}du = \int_0^{f(x)}\exp(\frac{-u^2}{2x}+\frac{u^3}{3x^2}-...+\frac{(-1)^{m-1}u^m}{mx^{m-1}})du + O(x^{-s})\]

Answer 1

\[\int_0^{f(x)}{e^{-u}(1+\frac{u}{x})^x}du\]\[ = \int_0^{f(x)}\exp(\frac{-u^2}{2x}+\frac{u^3}{3x^2}-...+\frac{(-1)^{m-1}u^m}{mx^{m-1}})du + O(x^{-s})\]

Answer 2

now it's math isn't it? :D

Answer 3

its a CS question about computational complexity

Answer 4

big Omicron notation :-D