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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.

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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

1. Fourier, J., La theorie analytique de la chaleur, Paris (1822). (See The analytical theory of heat Trans. Freeman, A., Dover, New York, 1955.)Google Scholar
2. Stephenson, G., Mathematical methods for science students, 2nd ed. Longman (1973).Google Scholar
3. Grattan-Guinness, I., The development of the foundations of mathematical analysis from Euler to Riemann, MIT Press, Cambridge, Mass. (1970).Google Scholar
4. Bromwich, T-J.I.A., An Introduction to the theory of infinite series, 2nd revised ed. Macmillan (1926).Google Scholar
5. Fitt, A.D. and Hoare, G.T.Q., The closed-form integration of arbitrary functions, Math. Gaz. 77 (July 1993) pp. 227–236.10.2307/3619719Google Scholar
6. Herbert, E. and Tin, S.K., The Lobachevskiy’s function and related integrals, Inst, of Math, and its Applications Bulletin 27 (1991) p. 175–180.Google Scholar
7. Abramowitz, M. and Stegun, I.A., Handbook of mathematical functions, Dover, New York (1965).Google Scholar
8. Hardy, G.H., Pure mathematics, Cambridge, 10th edn. (1952).Google Scholar
9. Courant, R. and Robbins, H., What is mathematics? Oxford (1941).Google Scholar