In mathematics, the Clausen function is defined by the following integral: Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
More generally, one defines
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It is related to the polylogarithm by The polylogarithm (also known as Jonquiéres function) is a special function and may be defined for all s and |z|<1 by: Both the parameter s and the argument z are taken to be complex numbers. ...
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Ernst Kummer and Rogers give the relation Ernst Eduard Kummer (29 January 1810 in Sorau, Brandenburg, Prussia - 14 May 1893 in Berlin, Germany) was a German mathematician. ...
valid for .
For rational values of θ / π (that is, for θ / π = p / q for some integers p and q), the function sin(nθ) can be understood to represent a periodic orbit of an element in the cyclic group, and thus can be expressed as a simple sum involving the Hurwitz zeta function. In mathematics, a cyclic group is a group that can be generated by a single element, in the sense that the group has an element a (called a generator of the group) such that every element of the group is a power of a. ... In mathematics, the Hurwitz zeta function is one of the many zeta functions. ...
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