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The accurate summation of some awkward series
Published online by Cambridge University Press: 01 August 2016
Extract
In 1822 Joseph Fourier published an account of his work on the mathematical theory of heat. In his book Fourier considered the representation of a function f(x), which is defined on an interval such as 0 
x < 2π, by an infinite sum of trigonometric functions:
where the trailing dots indicate the sum goes on forever. The series is written more concisely with sigma notation as
where x is restricted to an interval such as 0 x < 2π, and a0, an and bn are constant coefficients.
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