Suppose it is known that the coefficients in the expansion and express this in terms of familiar elementary functions. f(x) = anx" n=0 satisfy (n + 2)an+1x" -anx" = 0. n=0 n=0 Show that ao f(x) = 1 "+1 (n + 1)! n=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose it is known that the coefficients in the
expansion
and express this in terms of familiar elementary
functions.
f(x) = anx"
n=0
satisfy
(n + 2)an+1x" -anx" = 0.
n=0
n=0
Show that
ao
f(x) =
1
"+1
(n + 1)!
n=0
Transcribed Image Text:Suppose it is known that the coefficients in the expansion and express this in terms of familiar elementary functions. f(x) = anx" n=0 satisfy (n + 2)an+1x" -anx" = 0. n=0 n=0 Show that ao f(x) = 1 "+1 (n + 1)! n=0
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