Index
Notations
Search
Need Help?
How to Cite
Customize
Annotate
UnAnnotate
About the Project
Chapter 18
Orthogonal Polynomials
Notes:
The main references for writing this chapter are
Andrews
et al.
(
1999
)
,
Askey and Wilson (
1985
)
,
Chihara (
1978
)
,
Koekoek
et al.
(
2010
)
, and
Szegö (
1975
)
.
Referenced by:
§14.7(i)
,
§16.7
,
§3.11(ii)
,
René F. Swarttouw
,
Roelof Koekoek
,
Roderick S. C. Wong
,
Tom H. Koornwinder
,
Organization and Objective
,
§
‣
§
Software Cross Index
Permalink:
http://dlmf.nist.gov/18
T. H. Koornwinder
University of Amsterdam, Korteweg–de Vries Institute, Amsterdam, The Netherlands.
R. Wong
City University of Hong Kong, Liu Bie Ju Centre for Mathematical Sciences, Kowloon, Hong Kong.
R. Koekoek
Delft University of Technology, Delft Institute of Applied Mathematics, Delft, The Netherlands.
R. F. Swarttouw
Vrije Universiteit Amsterdam, Department of Mathematics, Amsterdam, The Netherlands.
Notation
18.1
Notation
General Orthogonal Polynomials
18.2
General Orthogonal Polynomials
Classical Orthogonal Polynomials
18.3
Definitions
18.4
Graphics
18.5
Explicit Representations
18.6
Symmetry, Special Values, and Limits to Monomials
18.7
Interrelations and Limit Relations
18.8
Differential Equations
18.9
Recurrence Relations and Derivatives
18.10
Integral Representations
18.11
Relations to Other Functions
18.12
Generating Functions
18.13
Continued Fractions
18.14
Inequalities
18.15
Asymptotic Approximations
18.16
Zeros
18.17
Integrals
18.18
Sums
Askey Scheme
18.19
Hahn Class: Definitions
18.20
Hahn Class: Explicit Representations
18.21
Hahn Class: Interrelations
18.22
Hahn Class: Recurrence Relations and Differences
18.23
Hahn Class: Generating Functions
18.24
Hahn Class: Asymptotic Approximations
18.25
Wilson Class: Definitions
18.26
Wilson Class: Continued
Other Orthogonal Polynomials
18.27
-Hahn Class
18.28
Askey–Wilson Class
18.29
Asymptotic Approximations for
-Hahn and Askey–Wilson Classes
18.30
Associated OP’s
18.31
Bernstein–Szegö Polynomials
18.32
OP’s with Respect to Freud Weights
18.33
Polynomials Orthogonal on the Unit Circle
18.34
Bessel Polynomials
18.35
Pollaczek Polynomials
18.36
Miscellaneous Polynomials
18.37
Classical OP’s in Two or More Variables
Applications
18.38
Mathematical Applications
18.39
Physical Applications
Computation
18.40
Methods of Computation
18.41
Tables
18.42
Software