Tea Time Numerical Analysis · Problem 1.2.20

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · maclaurin-polynomial

Problem

For f(x)=tan⁡−1(x)f(x) = \tan^{-1}(x), f(n)(0)={0if n is even(−1)(n−1)/2(n−1)!if n is odd.f^{(n)}(0) = \begin{cases} 0 & \text{if } n \text{ is even} \\ (-1)^{(n-1)/2}(n-1)! & \text{if } n \text{ is odd.} \end{cases} Find the nthn^{th} Maclaurin polynomial Pn(x)P_n(x) for ff.

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