Using the Eigenfunctions of the Previous Problem, the Fourier-Legendre Series $f ( x )$

question 29

Multiple Choice

Using the eigenfunctions of the previous problem, the Fourier-Legendre series for the function $f ( x )$ is $\sum _ { n = 1 } ^ { \infty } c _ { n } P _ { n } ( x )$ , where

• A) \(c _ { n } = ( 2 n + 1 ) \int _ { - 1 } ^ { 1 } x f ( x ) P _ { n } ( x ) d x\)
• B) \(c _ { n } = ( 2 n + 1 ) \int _ { - 1 } ^ { 1 } f ( x ) P _ { n } ( x ) d x\)
• C) \(c _ { n } = ( 2 n + 1 ) \int _ { - 1 } ^ { 1 } f ( x ) P _ { n } ( x ) d x / 2\)
• D) \(c _ { n } = ( 2 n - 1 ) \int _ { - 1 } ^ { 1 } f ( x ) P _ { n } ( x ) d x / 2\)
• E) \(c _ { n } = ( 2 n - 1 ) \int _ { - 1 } ^ { 1 } x f ( x ) P _ { n } ( x ) d x\)