| Tho I don't see any obvious solution, it may be based on Parseval's
equation. This states that the energy in a periodic function f(t)
over its period must equal the energy of all its Fourier coefficients.
---
/ 2 \ 2
| f(t) dt = > |c |
/ / n
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Say you had f(t) which gave rise to set of Fourier coefficients
which happened to be the roots of tan(r) = r... Then if f(t)^2 could
be integrated in closed form over one period you'd have a proof. This is one
popular way of summing series (such as 1/n^2) since such series
often result from simple f(t)'s such as triangle waves, sawtooth
waves, etc.
The roots of tan(r) = r also have other suspicious connections; I remember
they're the eigenvalues of a certain boundry value problem so that
might help (i don't remember which one though)
- Jim
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