Show that ifjis an odd function on the interval (-1, 1), then (21) and (22) become
Chapter 12, Problem 20(choose chapter or problem)
Show that ifjis an odd function on the interval (-1, 1), then (21) and (22) become, respectively, 00 f(x) = LC2n+1P2n+1(x) (27) n=O c2n+l = (4n + 3) ft(x)P2n+1(x) dx. (28) The series (25) and (27) can also be used when f is defined on only the interval (0, 1 ). Both series represent! on (0, 1 ); but on the interval (-1, 0), (25) represents an even extension, whereas (27) represents an odd extension. In 21 and 22, write out the first four nonzero terms in the indicated expansion of the given function. What function does the series represent on the interval (-1, 1)? Use a CAS to graph the partial sum Six).
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