(a) Using the exponential series and the geometric series, determine a Taylor series for the function {(-) =-1, 1- z with zo = 0. For which z does this series converge? Hint: The Cauchy product of series is Ck = a,bk-t. 1=0 with i=0 j=0 k=0 (b) What is the order of the zero of this function at 0? Justify vour answer
(a) Using the exponential series and the geometric series, determine a Taylor series for the function {(-) =-1, 1- z with zo = 0. For which z does this series converge? Hint: The Cauchy product of series is Ck = a,bk-t. 1=0 with i=0 j=0 k=0 (b) What is the order of the zero of this function at 0? Justify vour answer
Chapter8: Sequences, Series,and Probability
Section8.1: Sequences And Series
Problem 9ECP: For the series i=1510i find (a) the fourth partial sum and (b) the sum. Notice in Example 9(b) that...
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Taylor series/theorem and zeros of complex functions
Transcribed Image Text:(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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