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(a: (b: 1) The Gegenbauer Polynomials with A= are a set of polynomials orthog- onal under the weighted inner product (f. 9)9 = √, f(x) g(x) (1 − x²) dr. - ) Produce the first 6 normalized Gegenbauer Polynomials with A= by applying the Gram-Schmidt Orthonormalization Procedure to the set S = {1, x, x2, x3, x4, 5} with the inner product above. ) Find the projection of f(x) = arctan(x) onto the first 6 normalized Gegenbauer Polynomials from 1(a). Show the integrals you need to compute to find the projection coefficients, but use Mathematica to evaluate them.

(a: (b: 1) The Gegenbauer Polynomials with A= are a set of polynomials orthog- onal under the weighted inner product (f. 9)9 = √, f(x) g(x) (1 − x²) dr. - ) Produce the first 6 normalized Gegenbauer Polynomials with A= by applying the Gram-Schmidt Orthonormalization Procedure to the set S = {1, x, x2, x3, x4, 5} with the inner product above. ) Find the projection of f(x) = arctan(x) onto the first 6 normalized Gegenbauer Polynomials from 1(a). Show the integrals you need to compute to find the projection coefficients, but use Mathematica to evaluate them.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 10E
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(a: (b: 1) The Gegenbauer Polynomials with A= are a set of polynomials orthog- onal under the weighted inner product (f. 9)9 = √, f(x) g(x) (1 − x²) dr. - ) Produce the first 6 normalized Gegenbauer Polynomials with A= by applying the Gram-Schmidt Orthonormalization Procedure to the set S = {1, x, x2, x3, x4, 5} with the inner product above. ) Find the projection of f(x) = arctan(x) onto the first 6 normalized Gegenbauer Polynomials from 1(a). Show the integrals you need to compute to find the projection coefficients, but use Mathematica to evaluate them.
Transcribed Image Text:(a: (b: 1) The Gegenbauer Polynomials with A= are a set of polynomials orthog- onal under the weighted inner product (f. 9)9 = √, f(x) g(x) (1 − x²) dr. - ) Produce the first 6 normalized Gegenbauer Polynomials with A= by applying the Gram-Schmidt Orthonormalization Procedure to the set S = {1, x, x2, x3, x4, 5} with the inner product above. ) Find the projection of f(x) = arctan(x) onto the first 6 normalized Gegenbauer Polynomials from 1(a). Show the integrals you need to compute to find the projection coefficients, but use Mathematica to evaluate them.
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