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" J o = - n2 f(x') sinnx' dx'. Jo Hence the terms of the series we obtain by term to term differentiation of (2) are equal in magnitude and opposite in sign to those of the uniformly convergent series for f"(x), and these series represent the differential... "
Proceedings of the Edinburgh Mathematical Society - Page 27
by Edinburgh Mathematical Society - 1901
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Proceedings of the Edinburgh Mathematical Society, Volumes 18-20

Edinburgh Mathematical Society - Electronic journals - 1900 - 410 pages
...\*f'(x)siunx'dx' Jo = -n[rf(x')coanx'dx' Jo = - ill f(x) cosna;' I - n2 f(x') sinnx' dx' L Jo Jo = -na f (x') sinnx' dx. Jo Hence the terms of the series we obtain...represent the differential coefficients of the function. §5. The questions discussed in the preceding paragraphs are of pure mathematical interest. There is...
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