Fourier series: Difference between revisions
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In [[mathematics]], the '''Fourier series''', named after [[Joseph Fourier]] (1768—1830), of a [[complex number|complex]]-valued [[periodic function]] ''f'' of a [[real number|real]] variable, is an [[infinite series]] | In [[mathematics]], the '''Fourier series''', named after [[Joseph Fourier]] (1768—1830), of a [[complex number|complex]]-valued [[periodic function]] ''f'' of a [[real number|real]] variable, is an [[infinite series]] | ||
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In what sense it may be said that this series converges to ''f''(''x'') is a somewhat delicate question. | In what sense it may be said that this series converges to ''f''(''x'') is a somewhat delicate question. | ||
Revision as of 13:01, 26 September 2007
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In mathematics, the Fourier series, named after Joseph Fourier (1768—1830), of a complex-valued periodic function f of a real variable, is an infinite series
defined by
where T is the period of f.
In what sense it may be said that this series converges to f(x) is a somewhat delicate question.