. Determine the radius of convergence of the series 1 anz" when: (a) a₁ = (log n)² (b) an = n! (c) an = +3m
. Determine the radius of convergence of the series 1 anz" when: (a) a₁ = (log n)² (b) an = n! (c) an = +3m
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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Question
![16. Determine the radius of convergence of the series an" when:
(a) an = (logn)²
(b) an = n!
n=1
(c) an = 4 +3m
(d) a₁ = (n!)³/(3n)!
[Hint: Use Stirling's formula, which says that
n!~ene" for some e > 0..]
(e) Find the radius of convergence of the hypergeometric series
F(a, 3₁ %; z) = 1 + a(a + 1) ... (a+n− 1)3(3+1) ··· (3 + n − 1) ¸n
n!y(y + 1) (y + n − 1)
n=1
Here a, 3 € C and y# 0,-1, -2,....](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F904caeb1-cd31-4dcf-9af8-09f5b2d51865%2Fbd5e4504-8452-427c-a6ac-f41abd36fcca%2Fea42fch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:16. Determine the radius of convergence of the series an" when:
(a) an = (logn)²
(b) an = n!
n=1
(c) an = 4 +3m
(d) a₁ = (n!)³/(3n)!
[Hint: Use Stirling's formula, which says that
n!~ene" for some e > 0..]
(e) Find the radius of convergence of the hypergeometric series
F(a, 3₁ %; z) = 1 + a(a + 1) ... (a+n− 1)3(3+1) ··· (3 + n − 1) ¸n
n!y(y + 1) (y + n − 1)
n=1
Here a, 3 € C and y# 0,-1, -2,....
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