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Title: Confluent Hypergeometric Function of the First Kind -- from Wolfram MathWorld

Open Graph Title: Confluent Hypergeometric Function of the First Kind -- from Wolfram MathWorld

X Title: Confluent Hypergeometric Function of the First Kind -- from Wolfram MathWorld

Description: The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the confluent hypergeometric differential equation. It is also known as Kummer's function of the first kind. There are a number of other notations used for the function (Slater 1960, p. 2), including F(alpha,beta,x) (Kummer 1836), M(a,b,z) (Airey and Webb 1918), Phi(a;b;z) (Humbert 1920), and infty; u(a,b,x) (Magnus and...

Open Graph Description: The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the confluent hypergeometric differential equation. It is also known as Kummer's function of the first kind. There are a number of other notations used for the function (Slater 1960, p. 2), including F(alpha,beta,x) (Kummer 1836), M(a,b,z) (Airey and Webb 1918), Phi(a;b;z) (Humbert 1920), and infty; u(a,b,x) (Magnus and...

X Description: The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the confluent hypergeometric differential equation. It is also known as Kummer's function of the first kind. There are a number of other notations used for the function (Slater 1960, p. 2), including F(alpha,beta,x) (Kummer 1836), M(a,b,z) (Airey and Webb 1918), Phi(a;b;z) (Humbert 1920), and infty; u(a,b,x) (Magnus and...

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DC.TitleConfluent Hypergeometric Function of the First Kind
DC.CreatorWeisstein, Eric W.
DC.DescriptionThe confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the confluent hypergeometric differential equation. It is also known as Kummer's function of the first kind. There are a number of other notations used for the function (Slater 1960, p. 2), including F(alpha,beta,x) (Kummer 1836), M(a,b,z) (Airey and Webb 1918), Phi(a;b;z) (Humbert 1920), and infty; u(a,b,x) (Magnus and...
DC.Date.Modified2003-05-25
DC.Subject33C15
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2003-05-25
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