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C α1 = lim Ω(7q+7)n+1 n-100 Ω(7q+6) a1 = 0 → - = lim Ω_(7q+6) ( 848 T την 1 ΣΠΠΩ-+1)-(a+1-4+1 h=0 k=1 ΠΩ-(q+1)t-qΩ-11+4 ΠΩ-(a+1)t-q +1 t=0 ΠΩ-(n+1)t-q + 1 Πιο Ω-(n+1)t-q =0 = ΠΩ(q+1)t-4 ΠΩ-(n+1)t-q + 1 7h ΣΠ ΠΡΟ h=0 k=1 8 Th Ω h=0 k=1 X 1 ·(q+1)k-(q+1)t-q 1 ΣΠΠΩ+-+-4 +1 +1 (3)

C α1 = lim Ω(7q+7)n+1 n-100 Ω(7q+6) a1 = 0 → - = lim Ω_(7q+6) ( 848 T την 1 ΣΠΠΩ-+1)-(a+1-4+1 h=0 k=1 ΠΩ-(q+1)t-qΩ-11+4 ΠΩ-(a+1)t-q +1 t=0 ΠΩ-(n+1)t-q + 1 Πιο Ω-(n+1)t-q =0 = ΠΩ(q+1)t-4 ΠΩ-(n+1)t-q + 1 7h ΣΠ ΠΡΟ h=0 k=1 8 Th Ω h=0 k=1 X 1 ·(q+1)k-(q+1)t-q 1 ΣΠΠΩ+-+-4 +1 +1 (3)

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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In this work, we deal with the following nonlinear difference equation m-(7g+6) Im+l = m = 0,1, .., (1) where N-(79+6), S-(7+5), .., N-1, No e (0, 00) is investigated. (e) If (79+7)n+(t–1)q+t → a(t-1)q+t +0 then 2(7g+7)n+6q+7 →0 as n→ o, If (79+7)n+eg+t → argtt #0 then (7g+7)n+7q+7 + 0 as n → oo. t = 1,6. (d) We can generate the following formulas: 179+7)n+r(a+1)+s+1 = 2r-7)(9+1)+s+1 (1- (ITIm=1 2-(mg+m-1)+s)/{r-7)(q+1)+s+1 1+ (IIm-12-(mq+m-1)+s) n 7h+r 1 ΣΠ IIm-l la+1)t-(mq+m-1)+s +1 h=0 k=1 m%3D1 (e) Suppose that a1 = aq+2 a2g+3 = a39+4 = a4q+5 a5q+6 = a6g+7 0. By (d), we produce the following formulas below: II-o 2-(a+1)t-g 1- lim N17g+7)n+1 = lim 2-(7q+6) II-, 2-(a+1)t-g +1 n-00 7h 1 ΣΠ h=0 k=1 110 2-(a+1)k-(q+1)t-q +1 7h II-o 2-(9+1)t-ql-11+g 00 1 a1 = 2-(79+6) 2I,2-(4+1)k-(a+1)t-q + 1 - IT-o 2-(a+1)t-q +1 h=0 k=1 7h II-o 2-(9+1)t-g +1 II-o 2-(a+1)t-a 1 ΣΠ a1 = 0= (3) II-o P(a+1)k-(a+1)t-q +1 h=0 k=1 It=D0 6.
Transcribed Image Text:In this work, we deal with the following nonlinear difference equation m-(7g+6) Im+l = m = 0,1, .., (1) where N-(79+6), S-(7+5), .., N-1, No e (0, 00) is investigated. (e) If (79+7)n+(t–1)q+t → a(t-1)q+t +0 then 2(7g+7)n+6q+7 →0 as n→ o, If (79+7)n+eg+t → argtt #0 then (7g+7)n+7q+7 + 0 as n → oo. t = 1,6. (d) We can generate the following formulas: 179+7)n+r(a+1)+s+1 = 2r-7)(9+1)+s+1 (1- (ITIm=1 2-(mg+m-1)+s)/{r-7)(q+1)+s+1 1+ (IIm-12-(mq+m-1)+s) n 7h+r 1 ΣΠ IIm-l la+1)t-(mq+m-1)+s +1 h=0 k=1 m%3D1 (e) Suppose that a1 = aq+2 a2g+3 = a39+4 = a4q+5 a5q+6 = a6g+7 0. By (d), we produce the following formulas below: II-o 2-(a+1)t-g 1- lim N17g+7)n+1 = lim 2-(7q+6) II-, 2-(a+1)t-g +1 n-00 7h 1 ΣΠ h=0 k=1 110 2-(a+1)k-(q+1)t-q +1 7h II-o 2-(9+1)t-ql-11+g 00 1 a1 = 2-(79+6) 2I,2-(4+1)k-(a+1)t-q + 1 - IT-o 2-(a+1)t-q +1 h=0 k=1 7h II-o 2-(9+1)t-g +1 II-o 2-(a+1)t-a 1 ΣΠ a1 = 0= (3) II-o P(a+1)k-(a+1)t-q +1 h=0 k=1 It=D0 6.
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