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Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n > 0, T(n + 2) 1 [T(n + 1) + T(n)] . We are interested in the long term behavior, i.e., what does T(n) look like as n → 0?

Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n > 0, T(n + 2) 1 [T(n + 1) + T(n)] . We are interested in the long term behavior, i.e., what does T(n) look like as n → 0?

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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Use the recurrence relation on T to  nd an equation for F.

1) Define the generating function of T as F(x) = T(n)x" n=0
Transcribed Image Text:1) Define the generating function of T as F(x) = T(n)x" n=0
Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n > 0, T(n + 2) = (T(n + 1) + T(n)] . We are interested in the long term behavior, i.e., what does T(n) look like as n → oo?
Transcribed Image Text:Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n > 0, T(n + 2) = (T(n + 1) + T(n)] . We are interested in the long term behavior, i.e., what does T(n) look like as n → oo?
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