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Saturday, 2010 September 4, 02:22 — mathematics

to save some integrating

For my own future reference, in case I lose the bit of paper on which I jotted it.

In a function of period 2π, a unit step discontinuity in the nth derivative at phase α contributes this to the Fourier series:

i (in e-ik(t-α) – i-n eik(t-α)) / (2πkn+1)

I haven’t the skill to prove this for general n, but then I’m unlikely to need it for n>2.

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