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3. Let ƒ be the function expansion for this function centred at xo = r. What is the radius of convergence of your series (as a function of r)? Check that x = 1 is the barrier to convergence. For each r ‡ 1 find the power series

3. Let ƒ be the function expansion for this function centred at xo = r. What is the radius of convergence of your series (as a function of r)? Check that x = 1 is the barrier to convergence. For each r ‡ 1 find the power series

Advanced Engineering Mathematics
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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[Ex5 Q3]Calculus question, could u please show me how to check x = 1 is the radius of convergence in this case? thnx :)

1 3. Let f be the function x. For each r ‡ 1 find the power series 1-x expansion for this function centred at xo = r. What is the radius of convergence of your series (as a function of r)? Check that x = 1 is the barrier to convergence. Solution. 1 1 – x 1—r— (x-r) 1 1 1-r 1 1 x-r 1-r 0 (x - r ) n (1 − p)n+1
Transcribed Image Text:1 3. Let f be the function x. For each r ‡ 1 find the power series 1-x expansion for this function centred at xo = r. What is the radius of convergence of your series (as a function of r)? Check that x = 1 is the barrier to convergence. Solution. 1 1 – x 1—r— (x-r) 1 1 1-r 1 1 x-r 1-r 0 (x - r ) n (1 − p)n+1
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