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Everything about Basic hypergeometric series
Q-analog of hypergeometric series
In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio of successive terms xn+1/xn is a rational function of n. If the ratio of successive terms is a rational function of qn, then the series is called a basic hypergeometric series. The number q is called the base. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Basic hypergeometric seriesA 5-minute orientation
- Skim a recent paper: Expansions of averaged truncations of basic hypergeometric seriesInfluential work since 2022
- Pick up a classic book: Ramanujan 125The most-reprinted book on the subject
- Read the landmark paper: Balanced3ϕ2Summation Theorems forU(n) Basic Hypergeometric SeriesCited 65 times
- Go sideways: Q-Bessel polynomialsA closely related topic
- Go sideways: Q-Pochhammer symbolA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Balanced3ϕ2Summation Theorems forU(n) Basic Hypergeometric Series
Parameter Augmentation for Basic Hypergeometric Series, II
Mock Jacobi forms in basic hypergeometric series
Lattice paths and multiple basic hypergeometric series
The Cauchy operator for basic hypergeometric series
Bisymmetric functions, Macdonald polynomials and basic hypergeometric series
Bijective proofs of basic hypergeometric series identities
Invariance groups of transformations of basic hypergeometric series
🆕 Influential since 2022
Expansions of averaged truncations of basic hypergeometric series
q-Supercongruences from squares of basic hypergeometric series
Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series
Some q-supercongruences from squares of basic hypergeometric series
Expansion formulas for multiple basic hypergeometric series over root systems
📚 Books worth reading
- 📕Ramanujan 125Krishnaswami Alladi, Frank Garvan · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Q-Bessel polynomials In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A…
- Q-Pochhammer symbol In the mathematical field of combinatorics, the q-Pochhammer symbol, also called the q-shifted factorial, is the product ( a ; q ) n = ∏ k = 0 n − 1 (…
- Elliptic hypergeometric series In mathematics, an elliptic hypergeometric series is a series ∑ c n {\displaystyle {\textstyle \sum c_{n}}} such that the ratio c n c n − 1 {\displaystyle…
- Dixon's identity In mathematics, Dixon's identity (or Dixon's theorem or Dixon's formula) is any of several different but closely related identities proved by A. C. Dixon…
- Bilateral hypergeometric series In mathematics, a bilateral hypergeometric series is a series ∑ n = − ∞ ∞ a n {\displaystyle \sum _{n=-\infty }^{\infty }a_{n}} summed over all integers…
- Jackson q-Bessel function In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a…
- Generalized hypergeometric function In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n {\displaystyle n} is a…
- Hahn–Exton q-Bessel function In mathematics, the Hahn–Exton q-Bessel function or the third Jackson q-Bessel function is a q-analog of the Bessel function, and satisfies the Hahn-Exton…