hypergeometric functions - ορισμός. Τι είναι το hypergeometric functions
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Τι (ποιος) είναι hypergeometric functions - ορισμός

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
  • Plot of the hypergeometric function 2F1(a,b; c; z) 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

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         
  • 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".
Generalized hypergeometric function         
Generalized Hypergeometric Functions; Bailey list; Hypergeometric sum; Generalized hypergeometric series; Generalised hypergeometric function; Generalised hypergeometric series; PFq; Confluent hypergeometric limit function; 0F1; 3F2
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.

Βικιπαίδεια

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). Every second-order linear ODE with three regular singular points can be transformed into this equation.

For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Erdélyi et al. (1953) and Olde Daalhuis (2010). There is no known system for organizing all of the identities; indeed, there is no known algorithm that can generate all identities; a number of different algorithms are known that generate different series of identities. The theory of the algorithmic discovery of identities remains an active research topic.