Ean(x – c)" - n=0 satisfy |an+1] lim = L. no an (a) Find the radius of convergence of > an(x – c)". n=0 (b) Find a power series for d :Ean(x – c)", dx n=0 and determine its radius of convergence. (c) Find a power series for an(x – c)" | dx, 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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(a) Find the radius of convergence of an(x − c)n. n=0 (b) Find a power series for ∞ d ∑ an(x − c)n, dx n=0 and determine its radius of convergence. (c) Find a power series for ∫ ( ∞) ∑ an(x − c)n dx, n=0 and determine its radius of convergence.
Question 2 Suppose that the coefficients of the power series
an(x – c)"
n=0
satisfy
|an+1|
lim
= L.
Jan|
n00
(a) Find the radius of convergence of >an(x – c)".
n=0
(b) Find a power series for
d
dr an(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.
Transcribed Image Text:Question 2 Suppose that the coefficients of the power series an(x – c)" n=0 satisfy |an+1| lim = L. Jan| n00 (a) Find the radius of convergence of >an(x – c)". n=0 (b) Find a power series for d dr an(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.
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