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Express F in terms of functions that you know the power series expansion for

Express F in terms of functions that you know the power series expansion for

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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Can you answer number 3

Suppose that T(0) = a and T(1) = b and are some constants. Define the running pairwise average as, for n 2 0, 1 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 → 0? 1. Define the function of T as... F(x) = ) T(n) x"| n=0 Use the recurrence relation on T to find an equation for F. 2. Solve for F(x) 3. Express F in terms of functions that you know the power series expansion for 4. Give the power series expansion for F 5. Give a general form for T(n) for n2 2 6. What is the limit of T(n) as n → → o0?
Transcribed Image Text:Suppose that T(0) = a and T(1) = b and are some constants. Define the running pairwise average as, for n 2 0, 1 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 → 0? 1. Define the function of T as... F(x) = ) T(n) x"| n=0 Use the recurrence relation on T to find an equation for F. 2. Solve for F(x) 3. Express F in terms of functions that you know the power series expansion for 4. Give the power series expansion for F 5. Give a general form for T(n) for n2 2 6. What is the limit of T(n) as n → → o0?
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