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Abstract: By using computers to do experimental manipulations on Fourier series, weconstruct additional series with interesting properties. For example, weconstruct several series whose sums remain unchanged when the nth term ismultiplied by sinn-n. One series with this property is this classic seriesfor pi-4: pi-4 = 1 - 1-3 + 1-5

. = 1*sin1-1 - 1-3*sin3-3 +1-5*sin5-5



Another example is sum n = 1 to infinity of sinn-n =sum n = 1 to infinity of sinn-n^2 = pi - 1-2. This material should beaccessible to undergraduates.



Author: Robert Baillie

Source: https://arxiv.org/







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