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Everything about Hypergeometric function
Function defined by a hypergeometric series
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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Hypergeometric functionA 5-minute orientation
- Skim a recent paper: On the evaluation of the Appell F2 double hypergeometric functionInfluential work since 2022
- Pick up a classic book: Basic hypergeometric seriesThe most-reprinted book on the subject
- Read the landmark paper: On the hypergeometric matrix functionCited 133 times
- Go sideways: Riemann's differential equationA closely related topic
- Go sideways: Confluent hypergeometric functionA closely related topic
📖 Definitions
Noun Any function that is a solution of the hypergeometric equation; usually an expansion of an hypergeometric series
🏆 Landmark papers (most cited)
On the hypergeometric matrix function
Landen inequalities for Gaussian hypergeometric function
Lauricella's hypergeometric function FD
Generalized Hypergeometric Function of Unit Argument
Asymptotics of the hypergeometric function
Computing the Hypergeometric Function
GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
Numerical evaluation of Appell's hypergeometric function
🆕 Influential since 2022
On the evaluation of the Appell F2 double hypergeometric function
Asymptotics of Saran's hypergeometric function F
A parafermionic hypergeometric function and supersymmetric 6j-symbols
On Certain Integrals Related to Saran’s Hypergeometric Function FK
Fast calculation of scattering patterns using hypergeometric function algorithms
📚 Books worth reading
Basic hypergeometric seriesGeorge Gasper · 1990
The confluent hypergeometric functionHerbert Buchholz · 1969
Vorlesungen über die hypergeometrische FunktionFelix Klein · 1933- 📕The hypergeometric and Legendre functions with applications to integral equations of potential theoryChester Snow · 1942
- 📕Fonctions hypergéométriques et hypersphériquesPaul Appell · 1926
Tables of Airy functions and special confluent hypergeometric functions for asymptotic solutions of differential equations of the second orderA. D. Smirnov · 1960- 📕Generalized hypergeometric seriesWilfrid Norman Bailey · 1935
Hypergeometric SummationWolfram Koepf · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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