Proof. (a) Firstly, from (1), we get 2m+1 < Nm-(7g+6) for n e N, we get that there exist lim 2(7g+7)n-(7q+6)+t = a1+t;t = 0, 7q+ 6. n-00 (b) In view of the equation (1), L(7g+7)n-(7q+6) 1+ II?-o P(7g+7)n-(a+1)t-q L(7g+7)n+1 Then L(7q+7)n-(7q+6) lim 7g+7)n+1 = lim n00 1+ II-o (7q+7)n-(q+1)t-q n-00 6 II lim 2(7g+7)n-(a+1)t-q+i = 0, i = 0, q, n+00 t=0 or 6 Il (a+1)t+i = 0, i = 1, q + 1, t=0 is obtained.
Proof. (a) Firstly, from (1), we get 2m+1 < Nm-(7g+6) for n e N, we get that there exist lim 2(7g+7)n-(7q+6)+t = a1+t;t = 0, 7q+ 6. n-00 (b) In view of the equation (1), L(7g+7)n-(7q+6) 1+ II?-o P(7g+7)n-(a+1)t-q L(7g+7)n+1 Then L(7q+7)n-(7q+6) lim 7g+7)n+1 = lim n00 1+ II-o (7q+7)n-(q+1)t-q n-00 6 II lim 2(7g+7)n-(a+1)t-q+i = 0, i = 0, q, n+00 t=0 or 6 Il (a+1)t+i = 0, i = 1, q + 1, t=0 is obtained.
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:Proof.
(a) Firstly, from (1), we get 2m+1 < Nm-(7q+6) for n E N, we get that there exist
lim (7g+7)n-(7q+6)+t = a1+t,t = 0,7q + 6.
(b) In view of the equation (1),
L(7q+7)n-(7q+6)
1+ II-o P(7q+7)n-(q+1)t-q
P(7a+7)n+1
Then
L(7q+7)n-(7q+6)
lim 2(7g+7)n+1
lim
n+00 1+II-0 2(7q+7)n-(q+1)t-ą
n-00
Lt=0
|| lim 2(7g+7)n-(q+1)t-q+i
= 0, i = 0, q,
t=0
or
6
Ila(a+1)t+i = 0, i = 1, q + 1,
t=0
is obtained.
3
Transcribed Image Text:In this work, we deal with the following nonlinear difference equation
Im-(7q+6)
1+II-, 2m-(g+1)t-q
Im+1 =
т 3D0, 1, ...,
(1)
t%3D0
where N-(7g+6):, N-(7g+5), .., N1, No E (0, 00) is investigated.
(b)
6
II lim 2(7a+7)n-(q+1)t-q+i = 0, i = 0, q,
n00
t=0
or
6
I a(a+1)t+i =
0,
i = 1, q+1.
t=0
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