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What (who) is hypergeometric function - definition
Hypergeometric function
 with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200)
SPECIAL FUNCTION DEFINED BY A HYPERGEOMETRIC SERIES
Schwarz s-map; Euler hypergeometric integral; Gauss's hypergeometric theorem; Hypergeometric equation; Hypergeometric; Hypergeometric functions; Gauss hypergeometric theorem; Gauss hypergeometric function; Kummer's formula; Kummer's quadratic transformation; Hypergeometric differential equations; Hypergeometric differential equation; Hypergeometric series; Gaussian hypergeometric series; Gauss's hypergeometric series; 2F1; Gauss's summation theorem; Gaussian hypergeometric function
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE).
Confluent hypergeometric function
 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?width=200 "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")
SOLUTION OF A CONFLUENT HYPERGEOMETRIC EQUATION
Confluent hypergeometric functions; Kummer's series; Confluent hypergeometric series; Kummer series; Confluent hypergeometric equation; Kummer U function; 1F1; Tricomi Confluent hypergeometric function; Tricomi confluent hypergeometric function; Tricomi hypergeometric function; Tricomi function; Degenerated hypergeometric function; Kummer's equation
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".
General hypergeometric function
HYPERGEOMETRIC FUNCTION IN MATHEMATICS
Gelfand hypergeometric function; Aomoto–Gel'fand hypergeometric function; Aomoto–Gelfand hypergeometric function; Aomoto-Gelfand hypergeometric function; Aomoto-Gel'fand hypergeometric function
In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by . The general hypergeometric function is a function that is (more or less) defined on a Grassmannian, and depends on a choice of some complex numbers and signs.
