Show that if f is an odd function on the interval (1, 1), then (21) and (22) become
Chapter 12, Problem 20(choose chapter or problem)
Show that if f is an odd function on the interval (-1, 1), then (21) and (22) become, respectively,
\(\begin{gathered}
f(x)=\sum_{n=0}^{\infty} c_{2 n+1} P_{2 n+1}(x) \\
c_{2 n+1}=(4 n+3) \int_{0}^{1} f(x) P_{2 n+1}(x) d x .
\end{gathered}\)
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