(b) Given the power series f(x)=1-x-2x³ - 4x4 To(x) = 1 T₁(x) = x T₂(x) = 2x² - 1 T3(x) 4x²-3x = T₁(x) 8x48x²+1, = and the Chebyshev polynomials economize the power series f(x) twice.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(b) Given the power series
f(x)=1-x-2x³ - 4x4
To(x) =
1
T₁(x) =
X
T₂(x)
2x²1
=
T3(x)
4x³ - 3x
=
T4(x) =
8x4 _ 8x2 + 1,
and the Chebyshev polynomials
economize the power series f(x) twice.
Transcribed Image Text:(b) Given the power series f(x)=1-x-2x³ - 4x4 To(x) = 1 T₁(x) = X T₂(x) 2x²1 = T3(x) 4x³ - 3x = T4(x) = 8x4 _ 8x2 + 1, and the Chebyshev polynomials economize the power series f(x) twice.
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