About: Confluent hypergeometric function

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In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. The term confluent refers to the merging of singular points of families of differential equations; confluere is Latin for "to flow together". There are several common standard forms of confluent hypergeometric functions:

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rdfs:label	Confluent hypergeometric function (en) Fonction hypergéométrique confluente (fr) Equazione ipergeometrica confluente (it) 合流超几何函数 (zh)
rdfs:comment	在特殊函数中，合流超几何函数（confluent hypergeometric function）定义为合流超几何方程的解。它是高斯超几何函数的极限情形，相当于超几何方程中的两个正则奇点 1 和 ∞ 合流为一个非正则奇点 ∞，因而得名。根据所选择的参变量与宗量的不同，合流超几何函数有多种标准形式，常见的有： * Kummer 函数（第一类合流超几何函数）M(a,b,z) 是 Kummer 方程的解。注意有另一个相异且无关的函数也被称为 Kummer 函数； * Tricomi 函数（第二类合流超几何函数）U(a,b,z)是 Kummer 方程的另一个线性无关的解，有时会写成 Ψ(a,b,z)； * 惠泰克函数是惠泰克方程的解，惠泰克方程里的参数与 Kummer 方程的参数所对应的李代数参数相关； (zh) In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. The term confluent refers to the merging of singular points of families of differential equations; confluere is Latin for "to flow together". There are several common standard forms of confluent hypergeometric functions: (en) La fonction hypergéométrique confluente (ou fonction de Kummer) est :où désigne le symbole de Pochhammer. Elle est solution de l'équation différentielle d'ordre deux, appelée équation de Kummer : Elle est aussi définie par : (fr) In matematica, l'equazione ipergeometrica confluente o equazione di Kummer, da Ernst Kummer, è un'equazione differenziale lineare del secondo ordine ottenuta a partire dall'equazione di Papperitz-Riemann facendo confluire due singolarità in un solo punto; è strettamente legata con l'equazione ipergeometrica e le sue soluzioni, le funzioni ipergeometriche. Ciascuna delle soluzioni dell'equazione ipergeometrica confluente è analogamente chiamata funzione ipergeometrica confluente. (it)
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dcterms:subject	Hypergeometric functions Special functions Special hypergeometric functions
Wikipage page ID	1516095 (xsd:integer)
Wikipage revision ID	1107410865 (xsd:integer)
Link from a Wikipage to another Wikipage	Elementary function Meromorphic function Bessel function Binomial series Hypergeometric functions Hypergeometric function Beta distribution Cunningham function Hypergeometric differential equation Analytic function Mathematics Gauss's continued fraction Entire function Confluence Toronto function Singularity (mathematics) Kummer's function Airy function Edmund Taylor Whittaker Ernst Kummer Error function Formal power series Barnes integral Parabolic cylinder function Branch cut Regular singular point Hermite polynomials Asymptotic expansion Coulomb wave function Asymptotic Special functions Special hypergeometric functions Laguerre polynomial Laguerre polynomials Laplace transform Whittaker function Incomplete gamma function Sine integral Exponential integral Confluent hypergeometric limit function Linearly independent Multiplication theorem Rising factorial Bateman's function Asymptotic series Characteristic function (probability) Indicial equation Poisson–Charlier function Journal für die reine und angewandte Mathematik Whittaker's equation Generalized Laguerre polynomial Generalized hypergeometric series Bessel equation Bessel polynomial Hankel function Irregular singularity Kelvin function Logarithmic integral
Link from a Wikipage to an external page	http://dlmf.nist.gov/13 http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/ http://functions.wolfram.com/HypergeometricFunctions/HypergeometricU/ https://archive.org/details/confluenthyperge0000slat https://books.google.com/books%3Fid=UrSnNeJW10YC&pg=PA75 http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002141329
sameAs	Confluent hypergeometric function Confluent hypergeometric function Confluent hypergeometric function Confluent hypergeometric function Confluent hypergeometric function

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