Using the Eigenfunctions of the Previous Problem, Written As $g _ { n } ( x )$

Multiple Choice

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

A) $c _ { n } = \int _ { 0 } ^ { 2 } f ( x ) g _ { n } ( x ) d x / \int _ { 0 } ^ { 2 } g _ { n } ^ { 2 } ( x ) d x$
B) $c _ { n } = \int _ { 0 } ^ { 2 } x f ( x ) g _ { n } ( x ) d x / \int _ { 0 } ^ { 2 } g _ { n } ^ { 2 } ( x ) d x$
C) $c _ { n } = \int _ { 0 } ^ { 2 } f ( x ) g _ { n } ( x ) d x / \int _ { 0 } ^ { 2 } x g _ { n } ^ { 2 } ( x ) d x$
D) $c _ { n } = \int _ { 0 } ^ { 2 } x f ( x ) g _ { n } ( x ) d x / \int _ { 0 } ^ { 2 } x g _ { n } ^ { 2 } ( x ) d x$
E) $c _ { n } = \int _ { 0 } ^ { 2 } x ^ { 2 } f ( x ) g _ { n } ( x ) d x / \int _ { 0 } ^ { 2 } x ^ { 2 } g _ { n } ^ { 2 } ( x ) d x$