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Importing Wikidata short description: "Solution of a confluent hypergeometric equation" |
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{{Short description|Solution of a confluent hypergeometric equation}}
[[File:Plot of the Kummer confluent hypergeometric function 1F1(a;b;z) with a=1 and b=2 and input z² with 1F1(1,2,z²) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1.svg|alt=Plot of the Kummer confluent hypergeometric function 1F1(a;b;z) with a=1 and b=2 and input z² with 1F1(1,2,z²) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1|thumb|Plot of the Kummer confluent hypergeometric function 1F1(a;b;z) with a=1 and b=2 and input z² with 1F1(1,2,z²) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1]]
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 singular point|regular singularities]] merge into an [[irregular singularity]]. The term ''[[Confluence|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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