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The accurate summation of some awkward series

Published online by Cambridge University Press:  01 August 2016

Mark J. Cooker
Mark J. Cooker*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ
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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.

Type
Articles
Information
The Mathematical Gazette , Volume 82 , Issue 493 , March 1998 , pp. 48 - 55
Copyright
Copyright © Mathematical Association 1998 

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References

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