16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.5.4

Polynomials

Mathematics — Linear Algebra · generalized-taylor-formula

Problem

Prove the following generalization of Taylor's formula. Let ff, gg, and hh be polynomials over a subfield of the complex numbers, with deg⁡f≤n\deg f \leq n. Then f(g)=∑k=0n1k!f(k)(h)(g−h)k.f(g) = \sum_{k=0}^n \frac{1}{k!} f^{(k)}(h)(g-h)^k. (Here f(g)f(g) denotes 'ff of gg.')

Browse the problem library