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Title: Hypergeometric Function -- from Wolfram MathWorld

Open Graph Title: Hypergeometric Function -- from Wolfram MathWorld

X Title: Hypergeometric Function -- from Wolfram MathWorld

Description: A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ratio of successive terms can be written (c_(k+1))/(c_k)=(P(k))/(Q(k))=((k+a_1)(k+a_2)...(k+a_p))/((k+b_1)(k+b_2)...(k+b_q)(k+1))x. (1) (The factor of k+1 in the denominator is present for historical reasons of notation.) The function _2F_1(a,b;c;x) corresponding to p=2, q=1 is the first hypergeometric function to...

Open Graph Description: A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ratio of successive terms can be written (c_(k+1))/(c_k)=(P(k))/(Q(k))=((k+a_1)(k+a_2)...(k+a_p))/((k+b_1)(k+b_2)...(k+b_q)(k+1))x. (1) (The factor of k+1 in the denominator is present for historical reasons of notation.) The function _2F_1(a,b;c;x) corresponding to p=2, q=1 is the first hypergeometric function to...

X Description: A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ratio of successive terms can be written (c_(k+1))/(c_k)=(P(k))/(Q(k))=((k+a_1)(k+a_2)...(k+a_p))/((k+b_1)(k+b_2)...(k+b_q)(k+1))x. (1) (The factor of k+1 in the denominator is present for historical reasons of notation.) The function _2F_1(a,b;c;x) corresponding to p=2, q=1 is the first hypergeometric function to...

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DC.TitleHypergeometric Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionA generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ratio of successive terms can be written (c_(k+1))/(c_k)=(P(k))/(Q(k))=((k+a_1)(k+a_2)...(k+a_p))/((k+b_1)(k+b_2)...(k+b_q)(k+1))x. (1) (The factor of k+1 in the denominator is present for historical reasons of notation.) The function _2F_1(a,b;c;x) corresponding to p=2, q=1 is the first hypergeometric function to...
DC.Date.Modified2004-06-28
DC.Subject33C20
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/HypergeometricFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2004-06-28
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Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.http://www.amazon.com/exec/obidos/ASIN/0486612724/ref=nosim/ericstreasuretro
Mathematical Methods for Physicists, 3rd ed.http://www.amazon.com/exec/obidos/ASIN/0120598760/ref=nosim/ericstreasuretro
Generalised Hypergeometric Series.http://www.amazon.com/exec/obidos/ASIN/B0006VV1ME/ref=nosim/ericstreasuretro
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Basic Hypergeometric Series and Applications.http://www.amazon.com/exec/obidos/ASIN/0821815245/ref=nosim/ericstreasuretro
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Methods of Theoretical Physics, Part I.http://www.amazon.com/exec/obidos/ASIN/007043316X/ref=nosim/ericstreasuretro
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Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory.http://www.amazon.com/exec/obidos/ASIN/B0007F47LQ/ref=nosim/ericstreasuretro
An Atlas of Functions.http://www.amazon.com/exec/obidos/ASIN/0387488065/ref=nosim/ericstreasuretro
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