About: Particular values of the Riemann zeta function

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In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ(s) and is named after the mathematician Bernhard Riemann. When the argument s is a real number greater than one, the zeta function satisfies the equation

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rdfs:label	قيم خاصة لدالة زيتا لريمان (ar) Spezielle Werte der Riemannschen Zeta-Funktion (de) Constante zeta (es) Valeurs particulières de la fonction zêta de Riemann (fr) Costanti zeta (it) Particular values of the Riemann zeta function (en)
rdfs:comment	في الرياضيات، دالة زيتا لريمان هي دالة في التحليل العقدي، مهمة أيضا في نظرية الأعداد. عادة ما يرمز إليها بالرمز ζ(s). سُميت هكذا نسبة إلى عالم الرياضيات الألماني برنارد ريمان. عندما يكون المدخل s عددا حقيقيا أكبر قطعا من الواحد، تحقق دالة زيتا لريمان المعادلة التالية: (ar) En matemática, una constante zeta es el resultado de la función zeta de Riemann cuando esta se aplica sobre un número entero. (es) Die Riemannsche Zeta-Funktion ist eine mathematische Funktion, die eine besonders wichtige Rolle in der Zahlentheorie spielt. Für Werte kann sie definiert werden durch die Reihe In diesem Falle streben die einzelnen Summanden schnell genug gegen 0, sodass die Reihe gegen einen festen eindeutigen Wert konvergiert. Es ist ein klassisches mathematisches Problem, welche Werte die Zeta-Funktion an speziellen Stellen besitzt. Ein Beispiel hierfür ist das Basler Problem, das nach dem exakten Wert der Reihe aller kehrwertigen Quadratzahlen fragt, ergo dem Wert : (de) In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ(s) and is named after the mathematician Bernhard Riemann. When the argument s is a real number greater than one, the zeta function satisfies the equation (en) En mathématiques, la fonction zêta de Riemann est une fonction en analyse complexe, dont l'importance est notable en théorie des nombres. Elle est nommée d'après le mathématicien Bernhard Riemann et on la note souvent ζ(s). Pour un s réel supérieur à 1, elle est définie par Les valeurs de la fonction zêta listées ici incluent les valeurs de la fonction aux nombres entiers négatifs pairs (s = −2, −4, etc.), pour lesquels ζ(s) = 0 qui forment les zéros trivaux de la fonction. L'article consacré à la fonction détaille l'importance des zéros non triviaux pour la théorie des nombres. (fr) In matematica la funzione zeta di Riemann è una funzione che riveste grandissima importanza per la teoria dei numeri, a causa della sua relazione con la distribuzione dei numeri primi. Essa inoltre trova applicazioni in altre discipline, ad esempio nella fisica. Questo articolo fornisce un certo numero di rappresentazioni mediante serie dei valori della funzione zeta per argomenti interi. (it)
dcterms:subject	Irrational numbers Mathematical constants Zeta and L-functions
Wikipage page ID	2334098 (xsd:integer)
Wikipage revision ID	1118380534 (xsd:integer)
Link from a Wikipage to another Wikipage	Meromorphic function Basel problem Bernhard Riemann Bernoulli number Bernoulli numbers Apéry's theorem Irrational numbers Riemann hypothesis Riemann zeta function Complex analysis Complex number Complex plane Analytic continuation Mathematics Generating function Glaisher–Kinkelin constant Correlation function (statistical mechanics) Andrew Odlyzko Apéry's constant Harmonic series (mathematics) Pole (complex analysis) Simon Plouffe Mathematical constants Lambert series Zeta and L-functions Euler–Mascheroni constant Number theory Partial sum Particular values of the gamma function Ramanujan summation Residue (complex analysis) Heisenberg model (quantum) Arithmetic–geometric mean Zero (complex analysis) Digamma function Planck's law OEIS Real number Real part Stefan–Boltzmann law Series (mathematics) Complex derivative Wien approximation Russian Mathematical Surveys 1 + 2 + 3 + 4 + · · · Simple pole
Link from a Wikipage to an external page	http://wain.mi.ras.ru/PS/zeta5-11.pdf http://www.lacim.uqam.ca/~plouffe/inspired2.pdf http://www.lacim.uqam.ca/~plouffe/inspired22.html http://www.linas.org/math/plouffe-ram.pdf http://wain.mi.ras.ru/PS/zeta5-11$.pdf http://wain.mi.ras.ru/PS/zeta5-11.ps.gz https://web.archive.org/web/20090130142844/http:/www.lacim.uqam.ca/~plouffe/identities.html https://web.archive.org/web/20110926231624/http:/www.lacim.uqam.ca/~plouffe/inspired2.pdf http://www.dtc.umn.edu/~odlyzko/doc/zeta.html http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html http://www.lacim.uqam.ca/~plouffe/identities.html
sameAs	Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function Particular values of the Riemann zeta function
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date	2009-01-30 (xsd:date) 2011-09-26 (xsd:date)
url	https://web.archive.org/web/20090130142844/http:/www.lacim.uqam.ca/~plouffe/identities.html

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