33Dxx Basic hypergeometric functions
This subtopic studies basic hypergeometric functions, emphasizing q-analogues, special identities, and discrete deformation of classical theory.
Specific topics
33D05 $q$-gamma functions, $q$-beta functions and integrals
Overview
33D05 studies $q$-gamma functions, $q$-beta functions and integrals in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for $q$-gamma functions, $q$-beta functions and integrals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D15 Basic hypergeometric functions in one variable, ${}_r\phi_s$
Overview
33D15 studies basic hypergeometric functions in one variable, ${}_r\phi_s$ in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for basic hypergeometric functions in one variable, ${}_r\phi_s$
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D45 Basic orthogonal polynomials and functions
Overview
33D45 studies basic orthogonal polynomials and functions in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for basic orthogonal polynomials and functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D50 Orthogonal polynomials and functions in several variables
Overview
33D50 studies orthogonal polynomials and functions in several variables in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for orthogonal polynomials and functions in several variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D52 Basic orthogonal polynomials and functions associated with root systems
Overview
33D52 studies basic orthogonal polynomials and functions associated with root systems in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for basic orthogonal polynomials and functions associated with root systems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D60 Basic hypergeometric integrals and functions
Overview
33D60 studies basic hypergeometric integrals and functions in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for basic hypergeometric integrals and functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D65 Bibasic functions and multiple bases
Overview
33D65 studies bibasic functions and multiple bases in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for bibasic functions and multiple bases
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D67 Basic hypergeometric functions associated with root systems
Overview
33D67 studies basic hypergeometric functions associated with root systems in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for basic hypergeometric functions associated with root systems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D70 Other basic hypergeometric functions and integrals
Overview
33D70 studies other basic hypergeometric functions and integrals in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other basic hypergeometric functions and integrals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D80 Connections with quantum groups, Chevalley groups, $p$-adic groups
Overview
33D80 studies connections with quantum groups, chevalley groups, $p$-adic groups in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for connections with quantum groups, chevalley groups, $p$-adic groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks
33D90 Applications of basic hypergeometric functions
Overview
33D90 studies applications of basic hypergeometric functions in basic hypergeometric functions. It studies q-analogues of hypergeometric functions and their connections with combinatorics, partitions, and special-function identities.
Related Wikipedia Page
Basic Hypergeometric Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of basic hypergeometric functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in q-series, partition theory, and quantum algebra.
Applications
- q-series identities
- Partition and combinatorial theory
- Quantum and basic hypergeometric analysis
References
Recommended Textbooks