About: Meijer G-function

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In mathematics, the G-function was introduced by Cornelis Simon Meijer as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well. The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a line integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953.

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rdfs:label	Meijersche G-Funktion (de) Funzione G di Meijer (it) Meijer G-function (en) Meijer G-函数 (zh) G-функція Мейєра (uk)
rdfs:comment	Meijer G-函数是荷兰数学家梅耶尔引入的一种特殊函数。它是广义超几何函数的推广，绝大多数的特殊函数都可以用 Meijer G-函数表示出来。 (zh) Die G-Funktion wurde von Cornelis Simon Meijer (1904–1974) 1936 eingeführt. Die meisten bekannten speziellen Funktionen sind Spezialfälle dieser Funktion. Es gab auch andere Ansätze, die speziellen Funktionen zu verallgemeinern: Die verallgemeinerte hypergeometrische Funktion und die wurden zum gleichen Zweck vorgeschlagen. Die Meiersche G-Funktion umfasst diese beiden Funktionen als Spezialfall. In seiner ersten Definition verwendet Meijer eine Reihe. Die heute übliche, allgemeinere Definition erfolgt über ein Wegintegral in der komplexen Zahlenebene (siehe untenstehende Definition), die von Arthur Erdélyi 1953 vorgeschlagen wurde. Mit Hilfe dieser Definition und der Gamma-Funktion können die meisten speziellen Funktionen geschlossen dargestellt werden. (de) In mathematics, the G-function was introduced by Cornelis Simon Meijer as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well. The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a line integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953. (en) In matematica, la funzione G di Meijer è una funzione introdotta da nel 1936 con il proposito di definire una funzione molto generale che potesse includere come caso particolare la maggior parte delle funzioni speciali allora note. Questo non fu l'unico tentativo in questo senso: già la funzione ipergeometrica e la funzione E di MacRobert avevano lo stesso scopo, ma la funzione di Meijer andò oltre includendo anche queste altre funzioni come caso particolare. La prima definizione di Meijer fu fatta attraverso una serie; oggigiorno la definizione utilizzata è quella attraverso un opportuno integrale in campo complesso, ideato da Erdélyi nel 1953. Con la corrente formulazione, è possibile esprimere la maggior parte delle funzioni speciali in termini della funzione G di Meijer e della funzio (it) В математиці, G-функція що була введена Корнелісом Мейєром в 1936 році — дуже загальна функція, введена для того, що включити в себе більшість відомих спеціальних функцій як частковий випадок. Це не єдина спроба ввести таку функцію: the та мають таку ж ціль, однак G-функція Мейєра включає і їх в себе як частковий випадок. Перше означення було зроблене Мейєром з допомогою рядів; сьогодні прийняте більш загальне означення з допомогою інтегралу вздовж траєекторії в комплексній множині, введене в своїй повній загальності by в 1953 році. (uk)
foaf:depiction
dcterms:subject	Hypergeometric functions
Wikipage page ID	6453527 (xsd:integer)
Wikipage revision ID	1117443864 (xsd:integer)
Link from a Wikipage to another Wikipage	Elementary function Mellin transform Bessel function Derivative Hypergeometric functions Hypergeometric function Vector (mathematics and physics) Integral transform Complex plane Confluent hypergeometric function Holomorphic function Function (mathematics) Gamma function Generalized hypergeometric function GitLab Gradshteyn and Ryzhik Antiderivative Leonhard Euler Stirling's approximation Closure (mathematics) Computational algebra Functional equation Pole (complex analysis) Springer Publishing Line integral Fractional calculus Academic Press, Inc. Fox H-function Hankel transform Definite integral Residue (complex analysis) Heaviside step function Taylor series Arthur Erdélyi Laplace transform Whittaker function Special function Incomplete gamma function Lp space Ordinary differential equation Radius of convergence Rational number Mathematical singularity Series (mathematics) Ram Kishore Saxena Erdélyi–Kober operator Lerch transcendent Positive real axis Mellin–Barnes integral MacRobert E-function
Link from a Wikipage to an external page	https://archive.org/details/generalizedhyper0000unse http://apps.nrbook.com/bateman/Vol1.pdf https://gitlab.com/RZ-FZJ/hypergeom https://www.ams.org/journals/proc/1962-013-06/S0002-9939-1962-0144157-5/S0002-9939-1962-0144157-5.pdf https://www.ams.org/journals/proc/1963-014-01/S0002-9939-1963-0145263-2/S0002-9939-1963-0145263-2.pdf https://www.ams.org/journals/proc/1963-014-02/S0002-9939-1963-0149210-9/S0002-9939-1963-0149210-9.pdf https://www.ams.org/notices/201307/rnoti-p866.pdf
sameAs	Meijer G-function Meijer G-function Meijer G-function Meijer G-function Meijer G-function Meijer G-function Meijer G-function Meijer G-function
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