Let f(x) = X" and g(x) = x3 f (x2/25). Let anxn be the Taylor series of g about 0. The radius of convergence for the Taylor series for f is 1 and the radius of convergence n=1 the Taylor series for g is 5 Find each of the following coefficients the Taylor series for g. a4 = az = a2n+3 = ak = if k + 2n+3

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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Let f(x) = ) x"
and g(x) = x³ f (x²/25).
Let
anx"
be the Taylor series of g about 0. The radius of convergence for the Taylor series for f is 1
and the radius of convergence for
n=1
n=0
the Taylor series for g is 5
Find each of the following coefficients for the Taylor series for g.
a4 =
az =
a2n+3 =
ak
if k + 2n+3
II
Transcribed Image Text:00 00 Let f(x) = ) x" and g(x) = x³ f (x²/25). Let anx" be the Taylor series of g about 0. The radius of convergence for the Taylor series for f is 1 and the radius of convergence for n=1 n=0 the Taylor series for g is 5 Find each of the following coefficients for the Taylor series for g. a4 = az = a2n+3 = ak if k + 2n+3 II
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