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Confluent hypergeometric function

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…

Applications, Special cases & Kummer's equation

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Overview

Kummer's equation

Integral representations

Asymptotic behavior

Relations

Multiplication theorem

Connection with Laguerre polynomials and similar representations

Special cases

Application to continued fractions

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Confluent hypergeometric function

Nodes71
Edges70
Triples106
Avg. degree1.97
Density0.028169
Components1

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Confluent hypergeometric function

Top relations

related to References · 89
Confluent hypergeometric function → Abramowitz, Adri, An Atlas, Annali, Applicata, Applied Mathematics Series, Arthur, Atlas Function Calculator, Boisvert, Cambridge, Cambridge University Press, Chapter, Charles, Chistova, Clark, Commerce, Confluent, Consiglio Nazionale Delle Ricerche, Daniel, Date
related to External links · 4
Confluent hypergeometric function → Confluent Hypergeometric Functions, Mathematical FunctionsKummer, NIST Digital Library, Wolfram Functions
related to Other equations · 4
Confluent hypergeometric function → Confluent Hypergeometric Equation, Confluent Hypergeometric Functions, Extended Confluent Hypergeometric Equation, Note
related to Special cases · 3
Confluent hypergeometric function → Functions, Kummer, Some
is a · 1
Confluent hypergeometric function → solution of a confluent hypergeometric equation

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Important terminology

function equation functions solution kummer's hypergeometric confluent integer kummer asymptotic also differential second solutions mr integral two cases isbn 1837

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Confluent hypergeometric functionis asolution of a confluent hypergeometric equation0.90text
Airy functionsinstance ofBateman's functionBessel functions and many related functions0.80text
Kelvin functionsinstance ofBateman's functionBessel functions and many related functions0.80text
Hankel functionsinstance ofBateman's functionBessel functions and many related functions0.80text
the sine integralinstance ofCoulomb wave functionCunningham functionsExponential integral and related functions0.80text
logarithmic integralHermite polynomialsIncomplete gamma functionLaguerre polynomialsParabolic cylinder functioninstance ofCoulomb wave functionCunningham functionsExponential integral and related functions0.80text
Confluent hypergeometric functionrelated to External linksConfluent Hypergeometric Functions0.60section
Confluent hypergeometric functionrelated to External linksNIST Digital Library0.60section
Confluent hypergeometric functionrelated to External linksMathematical FunctionsKummer0.60section
Confluent hypergeometric functionrelated to External linksWolfram Functions0.60section
Confluent hypergeometric functionrelated to Other equationsConfluent Hypergeometric Functions0.60section
Confluent hypergeometric functionrelated to Other equationsExtended Confluent Hypergeometric Equation0.60section

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