Suppose that the coefficients of the power series Ean(r – c)" n=0 satisfy |an+1\| lim = L. |an| (a) Find the radius of convergence of an(x – c)". n=0 (b) Find a power series for d an(x – c)", dx n=0 and determine its radius of convergence. (c) Find a power series for an(x-c)" dx, n3D0 and determine its radius of convergence.
Suppose that the coefficients of the power series Ean(r – c)" n=0 satisfy |an+1\| lim = L. |an| (a) Find the radius of convergence of an(x – c)". n=0 (b) Find a power series for d an(x – c)", dx n=0 and determine its radius of convergence. (c) Find a power series for an(x-c)" dx, n3D0 and determine its radius of convergence.
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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Transcribed Image Text:Suppose that the coefficients of the power series
E an(x – c)"
n=0
satisfy
|an+1\
lim
= L.
|an|
n→∞
(a) Find the radius of convergence of > an(x
– c)".
|
n=0
I
(b) Find a power series for
dr Lan(x – c)".
n=0
and determine its radius of convergence.
(c) Find a power series for
an(x-c)"
dx,
and determine its radius of convergence.
8.
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