Explanation Given: The Fourier-Legendre series of an odd function f defined on the interval ( − 1 , 1 ) is as follows: f ( x ) = ∑ n = 0 ∞ c 2 n + 1 P 2 n + 1 ( x ) c 2 n + 1 = ( 4 n + 3 ) ∫ 0 1 f ( x ) P 2 n + 1 ( x ) d x Calculation: From Fourier-Legendre series the function f ( x ) is defined as follows: f ( x ) = ∑ n = 0 ∞ c 2 n + 1 P 2 n + 1 ( x ) ...... ( 1 ) The function c 2 n is defined as follows: c 2 n + 1 = ( 4 n + 3 ) ∫ 0 1 f ( x ) P 2 n + 1 ( x ) d x ...... ( 2 ) Substitute 0 for n in equation (2) and solve. c 1 = ( 4 ( 0 ) + 3 ) ∫ 0 1 f ( x ) P 1 ( x ) d x = 3 ∫ 0 1 1 ⋅ x d x = 3 ∫ 0 1 x d x = 3 2 Substitute 1 for n in equation (2) and solve

WEB ASSIGN FOR ZILL'S DIFFERENTIAL EQUAT

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ISBN: 9780357539545

Author: ZILL

Publisher: CENGAGE L

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Chapter 11.5, Problem 22E

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The first four nonzero terms in the Fourier-Legendre expansion for the function f(x)=1, 0<x<1 and also draw the graph.

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Chapter 11.5, Problem 21E

Chapter 11.5, Problem 23E

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Chapter 11 Solutions

WEB ASSIGN FOR ZILL'S DIFFERENTIAL EQUAT

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The first four nonzero terms in the Fourier-Legendre expansion for the function f ( x ) = 1 , 0 < x < 1 and also draw the graph.

Solution Summary: The author explains the Fourier-Legendre expansion for the function f(x)=1,0x1 and draws the graph. The sum of the first four nonzero terms in

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The first four nonzero terms in the Fourier-Legendre expansion for the function f(x)=1, 0<x<1 and also draw the graph.

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Chapter 11 Solutions

The first four nonzero terms in the Fourier-Legendre expansion for the function f ( x ) = 1 , 0 &lt; x &lt; 1 and also draw the graph.

Solution Summary: The author explains the Fourier-Legendre expansion for the function f(x)=1,0x1 and draws the graph. The sum of the first four nonzero terms in

Videos

The first four nonzero terms in the Fourier-Legendre expansion for the function f(x)=1, 0<x<1 and also draw the graph.

Want to see the full answer?

Chapter 11 Solutions

The first four nonzero terms in the Fourier-Legendre expansion for the function f ( x ) = 1 , 0 < x < 1 and also draw the graph.