33Exx Other special functions
This subtopic studies other special functions, collecting additional families that arise in analysis, mathematical physics, and asymptotic questions.
Specific topics
33E05 Elliptic functions and integrals
Overview
33E05 studies elliptic functions and integrals in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for elliptic 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 to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E10 Lamé, Mathieu, and spheroidal wave functions
Overview
33E10 studies lamã©, mathieu, and spheroidal wave functions in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for lamã©, mathieu, and spheroidal wave functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E12 Mittag-Leffler functions and generalizations
Overview
33E12 studies mittag-leffler functions and generalizations in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for mittag-leffler functions and generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E15 Other wave functions
Overview
33E15 studies other wave functions in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other wave functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E17 Painlevé-type functions
Overview
33E17 studies painlevã©-type functions in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for painlevã©-type functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E20 Other functions defined by series and integrals
Overview
33E20 studies other functions defined by series and integrals in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other functions defined by series 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 to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E25 Orthogonal polynomials and functions
Overview
33E25 studies orthogonal polynomials and functions in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for 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 to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E30 Other functions coming from differential, difference and integral equations
Overview
33E30 studies other functions coming from differential, difference and integral equations in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other functions coming from differential, difference and integral equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E50 Special functions in characteristic $p$
Overview
33E50 studies special functions in characteristic $p$ in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special functions in characteristic $p$
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks
33E99 None of the above
Overview
33E99 studies none of the above in other special functions. It covers special functions beyond the classical elementary and hypergeometric families, including orthogonal and transcendental examples.
Related Wikipedia Page
Other Special Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for none of the above
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize special-function identities, asymptotics, and transforms.
Applications
- Orthogonal and transcendental functions
- Asymptotic formulas
- Analytic identities and transforms
References
Recommended Textbooks