An infinite series of trigonometric functions which represents an expansion or approximation of a periodic function, used in Fourier analysis.
- Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes.
- In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.
- He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory.
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