S Siwasq13 New member Joined Apr 9, 2021 Messages 1 Apr 9, 2021 #1 Suppose f is an analytic function such that f[n](0)=n. Find f(1) I’m just not quite sure how to approach this problem, I may need a refresher on power/Taylor series, thanks in advance.

Suppose f is an analytic function such that f[n](0)=n. Find f(1) I’m just not quite sure how to approach this problem, I may need a refresher on power/Taylor series, thanks in advance.

H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 7,453 Apr 9, 2021 #2 Write f as a "MacLaurin series": \(\displaystyle f(x)= f(0)+ f'(0)x+ \frac{f"(0)}{2}x^2+ \cdot\cdot\cdot+ \frac{f^{[n]}(0)}{n!}x^n\).

Write f as a "MacLaurin series": \(\displaystyle f(x)= f(0)+ f'(0)x+ \frac{f"(0)}{2}x^2+ \cdot\cdot\cdot+ \frac{f^{[n]}(0)}{n!}x^n\).