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how how to expand the function f (x) = 2x4 – 3² + x + 7 %3D

how how to expand the function f (x) = 2x4 – 3² + x + 7 %3D

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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As an elementary application of the use of Chebyshev polynomials, we show how to expand the function f(х) — 2x4 — 3а? + х + 7 (7.74) in terms of these polynomials. First, we must invert the Chebyshev polynomi- als and express the various powers of x in terms of them. This is easily done, 224 Difference Equations and the following results are obtained: To(x) 1 = 2 = T1(x), 1 x² = T2(x) + 2' (7.75) 3 23 = T3(x) + T1(x), 4 3 a4 = T4(x) – T2(x) - The substitution of equations (7.75) into equation (7.74) gives f(x) = 2T4(x) – T2(x)+T1(x)+ To(x). 4 (7.76)
Transcribed Image Text:As an elementary application of the use of Chebyshev polynomials, we show how to expand the function f(х) — 2x4 — 3а? + х + 7 (7.74) in terms of these polynomials. First, we must invert the Chebyshev polynomi- als and express the various powers of x in terms of them. This is easily done, 224 Difference Equations and the following results are obtained: To(x) 1 = 2 = T1(x), 1 x² = T2(x) + 2' (7.75) 3 23 = T3(x) + T1(x), 4 3 a4 = T4(x) – T2(x) - The substitution of equations (7.75) into equation (7.74) gives f(x) = 2T4(x) – T2(x)+T1(x)+ To(x). 4 (7.76)
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