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- Clausen_function abstract "In mathematics, the Clausen function - introduced by Thomas Clausen (1832) - is a transcendental, special function of a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other special functions. It is intimately connected with the Polylogarithm, Inverse tangent integral, Polygamma function, Riemann Zeta function, Eta function, and Dirichlet beta function.The Clausen function of order 2 - often referred to at the Clausen function, despite being but one of a class of many - is given by the integral:In the range :the Sine function inside the absolute value sign remains strictly positive, so the absolute value signs may be omitted. The Clausen function also has the Fourier series representation:The Clausen functions - as a class of functions - feature extensively in many areas of modern mathematical research, particularly in relation to the evaluation of many classes of logarithmic and Polylogarithmic integrals, both definite and indefinite. They also have numerous applications with regard to the summation of Hypergeometric series, Central Binomial sums, sums of the Polygamma function, and Dirichlet L-series.".
- Clausen_function thumbnail Clausen-function.png?width=300.
- Clausen_function wikiPageExternalLink purl?PPN243919689_0008.
- Clausen_function wikiPageExternalLink borwein1.pdf.
- Clausen_function wikiPageExternalLink slac-pub-5809.pdf.
- Clausen_function wikiPageExternalLink nielsenrelations.pdf.
- Clausen_function wikiPageID "406899".
- Clausen_function wikiPageRevisionID "606298988".
- Clausen_function archive "hep-ph".
- Clausen_function authorlink "Thomas Clausen".
- Clausen_function first "Thomas".
- Clausen_function hasPhotoCollection Clausen_function.
- Clausen_function id "411100".
- Clausen_function last "Clausen".
- Clausen_function year "1832".
- Clausen_function subject Category:Zeta_and_L-functions.
- Clausen_function comment "In mathematics, the Clausen function - introduced by Thomas Clausen (1832) - is a transcendental, special function of a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other special functions.".
- Clausen_function label "Clausen function".
- Clausen_function label "Clausen-Funktion".
- Clausen_function label "Fonction de Clausen".
- Clausen_function sameAs Clausen-Funktion.
- Clausen_function sameAs Fonction_de_Clausen.
- Clausen_function sameAs m.024j_1.
- Clausen_function sameAs Q823290.
- Clausen_function sameAs Q823290.
- Clausen_function wasDerivedFrom Clausen_function?oldid=606298988.
- Clausen_function depiction Clausen-function.png.
- Clausen_function isPrimaryTopicOf Clausen_function.