Answered: Obtain the Taylor series ez = e Σ [(z…

Obtain the Taylor series ez = e Σ [(z - 1)^n / n!] (|z - 1| < ∞) for the function f(z) = ez by using f(n)(1) (n = 0, 1, 2, ...).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

Obtain the Taylor series

e^z = e Σ [(z - 1)^n / n!] (|z - 1| < ∞)

for the function f(z) = e^z

by using f⁽ⁿ⁾(1) (n = 0, 1, 2, ...).

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