(a) Using the exponential series and the geometric series, determine a Taylor series for the function f(2) = 1 1 with zo = 0. For which z does this series converge? Hint: The Cauchy product of series is α. Σ- Ck, with C => azbx-1- i=0 j=0 k=0 1=0 (b) What is the order of the zero of this function at z = 0? Justify your answer.

(a) Using the exponential series and the geometric series, determine a Taylor series for the function f(2) = 1 1 with zo = 0. For which z does this series converge? Hint: The Cauchy product of series is α. Σ- Ck, with C => azbx-1- i=0 j=0 k=0 1=0 (b) What is the order of the zero of this function at z = 0? Justify your answer.

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

(a) Using the exponential series and the geometric series, determine a Taylor series for
the function
f(2) =
1,
with zo = 0. For which z does this series converge?
Hint: The Cauchy product of series is
Ea: b; = > Ck;
Σ
with Ck = a¡bk–1-
i=0
j=0 k=0
l=0
(b) What is the order of the zero of this function at z = 0? Justify your answer,

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