Suppose that a power series f(x) = L a„x" n=0 has the radius of convergence p > 0 and that L.- anp" converges to a. Show that f(x) converges to a as x → p-.
Suppose that a power series f(x) = L a„x" n=0 has the radius of convergence p > 0 and that L.- anp" converges to a. Show that f(x) converges to a as x → p-.
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 a power series
00
f(x) = L anx"
%3D
n=0
has the radius of convergence p > 0 and that anp" converges to a.
Show that f(x) converges to a as x → p-.
n=0
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