hypergeometric function - translation to german
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hypergeometric function - translation to german

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         
Hypergeometrische Funktion, das Ergebnis einer hypergeometrischen Gleichung (Mathematik)
mathematical function         
  • A binary operation is a typical example of a bivariate function which assigns to each pair <math>(x, y)</math> the result <math>x\circ y</math>.
  • A function that associates any of the four colored shapes to its color.
  • Together, the two square roots of all nonnegative real numbers form a single smooth curve.
  • Graph of a linear function
  • The function mapping each year to its US motor vehicle death count, shown as a [[line chart]]
  • The same function, shown as a bar chart
  • Graph of a polynomial function, here a quadratic function.
  • Graph of two trigonometric functions: [[sine]] and [[cosine]].
  • right
ASSOCIATION OF A SINGLE OUTPUT TO EACH INPUT
Mathematical Function; Mathematical function; Function specification (mathematics); Mathematical functions; Empty function; Function (math); Ambiguous function; Function (set theory); Function (Mathematics); Functions (mathematics); Domain and range; Functional relationship; G(x); H(x); Function notation; Output (mathematics); Ƒ(x); Overriding (mathematics); Overriding union; F of x; Function of x; Bivariate function; Functional notation; Function of several variables; Y=f(x); ⁡; Draft:The Repeating Fractional Function; Image (set theory); Mutivariate function; Draft:Specifying a function; Function (maths); Functions (math); Functions (maths); F(x); Empty map; Function evaluation
mathematische Funktion
objective function         
IN STATISTICS, A FUNCTION REPRESENTING THE COST ASSOCIATED WITH AN EVENT
Objective function; Criterion function; Risk function; Quadratic loss function; Squared error loss; Loss functions; Stochastic criterion function; 0-1 loss function; Zero-one loss function; 0-1 loss; Zero-one loss; Loss Functions
objektive Funktion (Mathematik)

Definition

surjective

Wikipedia

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.