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

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.CT: Chapter Test
Problem 9CT
icon
Related questions
Question

Explain the determine blue

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)
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Basics (types, similarity, etc)
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage