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11: 13.28 Physical Applications

… ►

§13.28(i) Exact Solutions of the Wave Equation

… ►

§13.28(iii) Other Applications

►For dynamics of many-body systems see Meden and Schönhammer (1992); for tomography see D’Ariano et al. (1994); for generalized coherent states see Barut and Girardello (1971); for relativistic cosmology see Crisóstomo et al. (2004).

12: Alexander A. Its

… ►Current research areas of Its are mathematical physics, special functions, and integrable systems. …

13: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

14: Wolter Groenevelt

… ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. …

15: 8.23 Statistical Applications

§8.23 Statistical Applications

…

16: Peter A. Clarkson

… ►Clarkson has published numerous papers on integrable systems (primarily Painlevé equations), special functions, and symmetry methods for differential equations. …

17: Howard S. Cohl

… ►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and

q

-series. …

18: Bernard Deconinck

… ►He has worked on integrable systems, algorithms for computations with Riemann surfaces, Bose-Einstein condensates, and methods to investigate the stability of solutions of nonlinear wave equations. …

19: Tom H. Koornwinder

… ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …

20: 29.14 Orthogonality

… ►Secondly, the system of functions ►

29.14.1

f_{n}^{m}(s,t)=\mathit{uE}^{m}_{2n}\left(s,k^{2}\right)\mathit{uE}^{m}_{2n}% \left(K+\mathrm{i}t,k^{2}\right),

n=0,1,2,\dots

m=0,1,\dots,n

ⓘ

Defines:: $f_{n}^{m}(s,t)$ : system (locally)
Symbols:: $\mathit{uE}^{\NVar{m}}_{2\NVar{n}}\left(\NVar{z},\NVar{k^{2}}\right)$ : Lamé polynomial, $K\left(\NVar{k}\right)$ : Legendre’s complete elliptic integral of the first kind, $\mathrm{i}$ : imaginary unit, $m$ : nonnegative integer, $n$ : nonnegative integer and $k$ : real parameter
Referenced by:: §29.14
Permalink:: http://dlmf.nist.gov/29.14.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §29.14 and Ch.29

… ►Each of the following seven systems is orthogonal and complete with respect to the inner product (29.14.2): …In each system

n

ranges over all nonnegative integers and

m=0,1,\dots,n

. When combined, all eight systems (29.14.1) and (29.14.4)–(29.14.10) form an orthogonal and complete system with respect to the inner product …