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Let a sequence (Cn)n20 have a rational function S(x)/R(x) as its ordinary gener- ating function, where S(x) is a polynomial and R(x) = (1 – x)²(1+x). Assume that S(x) is not divisible either by 1– x or by 1+x. Give an asymptotic estimate of en of the form Cn = 0(f(n)), for a simple function f(n). |

Let a sequence (Cn)n20 have a rational function S(x)/R(x) as its ordinary gener- ating function, where S(x) is a polynomial and R(x) = (1 – x)²(1+x). Assume that S(x) is not divisible either by 1– x or by 1+x. Give an asymptotic estimate of en of the form Cn = 0(f(n)), for a simple function f(n). |

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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Let a sequence (Cn)n>0 have a rational function S(x)/R(x) as its ordinary gener- ating function, where S(x) is a polynomial and R(x) = (1 – x)²(1+x). Assume that S(x) is not divisible either by 1-x or by 1+x. Give an asymptotic estimate of the form Cn of Cn = 0(f(n)), for a simple function f(n).
Transcribed Image Text:Let a sequence (Cn)n>0 have a rational function S(x)/R(x) as its ordinary gener- ating function, where S(x) is a polynomial and R(x) = (1 – x)²(1+x). Assume that S(x) is not divisible either by 1-x or by 1+x. Give an asymptotic estimate of the form Cn of Cn = 0(f(n)), for a simple function f(n).
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