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Everything about Generalized hypergeometric function
Family of power series in mathematics
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by is a rational function of. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation. The generalized hypergeometric series is sometimes just called the hypergeometric series, though this term also sometimes just refers to the Gaussian hypergeometric series. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Generalized hypergeometric functionA 5-minute orientation
- Skim a recent paper: Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential EquationsInfluential work since 2022
- Pick up a classic book: Hypergeometric Functions, My LoveThe most-reprinted book on the subject
- Read the landmark paper: The Asymptotic Expansion of the Generalized Hypergeometric FunctionCited 249 times
- Go sideways: Bilateral hypergeometric seriesA closely related topic
- Go sideways: Meijer G-functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The Asymptotic Expansion of the Generalized Hypergeometric Function
The Asymptotic Expansion of the Generalized Hypergeometric Function
Classes of analytic functions associated with the generalized hypergeometric function
Generalized Hypergeometric Functions
Some results on a generalized hypergeometric function
Generalized Hypergeometric Function of Unit Argument
Inequalities and monotonicity of ratios for generalized hypergeometric function
Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
🆕 Influential since 2022
Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations
A study of generalized hypergeometric Matrix functions via two-parameter Mittag–Leffler matrix function
Generalized Brézin–Gross–Witten tau-function as a hypergeometric solution of the BKP hierarchy
On Analytical Extension of Generalized Hypergeometric Function 3F2
On the Relation between Lambert W-Function and Generalized Hypergeometric Functions
📚 Books worth reading
- 📕Hypergeometric Functions, My LoveMasaaki Yoshida · 2013
The major counting of nonintersecting lattice paths and generating functions for tableauxC. Krattenthaler · 1995- 📕Singularités des Systèmes Différentiels de Gauss-Maninédéric Pham · 2013
Path functions and generalized basic hypergeometric functionsKevin W. J. Kadell · 1987
Path functions and generalized basic hypergeometric functionsKevin W. J. Kadell · 1987
Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences (Lecture Notes in Mathematics)A. M. Mathai, R. K. Saxena · 1973
Analytic and combinatorial generalizations of the Rogers-Ramanujan identitiesDavid M. Bressoud · 1980- 📕Advanced complex analysisBarry Simon · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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