Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

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…

History, Special cases & The hypergeometric differential equation

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Hypergeometric function. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

History

The hypergeometric series

Special cases

The hypergeometric differential equation

Integral formulas

Values at special points z

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Hypergeometric function

Nodes81
Edges80
Triples49
Avg. degree1.98
Density0.024691
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Hypergeometric function

Top relations

related to External links · 17
Hypergeometric function → Computation, Doron Zeilberger, EMS Press, Encyclopedia, Eric, Herbert Wilf, Hypergeometric, Hypergeometric Functions, John Pearson, Marko Petkovsek, Mathematics, MathWorld, MSc Thesis, Oxford, The, University, Weisstein
related to John transform · 5
Hypergeometric function → Gelfand, Gindikin, Graev, John, The Gauss
related to Kummer's theorem (z = −1) · 5
Hypergeometric function → Ernst Kummer, Gamma, Gauss's, Kummer's, There
related to Other points · 5
Hypergeometric function → Gessel, Koepf, Some, Stanton, There
related to Quadratic transformations · 4
Hypergeometric function → Goursat, If, Kummer, The
related to Higher order transformations · 3
Hypergeometric function → Goursat, If, The
related to Special cases · 3
Hypergeometric function → Many, Some, When
related to The hypergeometric differential equation · 2
Hypergeometric function → Euler's, The
is a · 1
Hypergeometric function → solution of Euler's hypergeometric differential equation z
related to Gauss's continued fraction · 1
Hypergeometric function → Gauss

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle hypergeometric function equation frac points solutions series right left 1-z functions tfrac special singular monodromy linear group differential given

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hypergeometric functionis asolution of Euler's hypergeometric differential equation z0.90text
Hypergeometric functionrelated to External linksHypergeometric0.60section
Hypergeometric functionrelated to External linksEncyclopedia0.60section
Hypergeometric functionrelated to External linksMathematics0.60section
Hypergeometric functionrelated to External linksEMS Press0.60section
Hypergeometric functionrelated to External linksJohn Pearson0.60section
Hypergeometric functionrelated to External linksComputation0.60section
Hypergeometric functionrelated to External linksHypergeometric Functions0.60section
Hypergeometric functionrelated to External linksUniversity0.60section
Hypergeometric functionrelated to External linksOxford0.60section
Hypergeometric functionrelated to External linksMSc Thesis0.60section
Hypergeometric functionrelated to External linksMarko Petkovsek0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.