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The uniqueness and the zeros of trigonometric series was an active area of research in 19th century Europe. First, Georg Cantor proved that if a trigonometric series is convergent to a function on the interval [,], which is identically zero, or more generally, is nonzero on at most finitely many points, then the coefficients of the series are all zero.
In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy (from Alexandria, Egypt) constructed detailed trigonometric tables (Ptolemy's table of chords) in Book 1, chapter 11 of his Almagest. [11] Ptolemy used chord length to define his trigonometric functions, a minor difference from the sine convention we use today. [12] (The value we call ...
Nina Karlovna Bari (Russian: Нина Карловна Бари; 19 November 1901 – 15 July 1961) was a Soviet mathematician known for her work on trigonometric series. [ 1 ] [ 2 ] She is also well-known for two textbooks, Higher Algebra and The Theory of Series .
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. It has some relationship to geometry , though there is disagreement on exactly what that relationship is; for some, trigonometry is just a subtopic of ...
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions.
The following outline is provided as an overview of and topical guide to trigonometry: . Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles.
Pages for logged out editors learn more. Contributions; Talk; Trigonometrical series