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… ► Eitner), published by Springer in 2000, and Discrete Differential Geometry: Integrable Structure (with Y. …He is also coeditor of Discrete Integrable Geometry and Physics (with R. Seiler), published by Oxford University Press in 1999, and Discrete Differential Geometry (with P. …
… ►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. …
§18.27(vii) Discrete -Hermite I and II Polynomials►
Discrete -Hermite I… ►
Discrete -Hermite II… ►
18.27.24 .►(For discrete -Hermite II polynomials the measure is not uniquely determined.)
… ►It is a discrete analog of theta functions. If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)): …This is the discrete analog of the Poisson identity (§1.8(iv)). …
Singularity analysis of generating functions.
SIAM J. Discrete Math. 3 (2), pp. 216–240.
From continuous to discrete Painlevé equations.
J. Math. Anal. Appl. 180 (2), pp. 342–360.
Discrete Painlevé equations and their appearance in quantum gravity.
Comm. Math. Phys. 142 (2), pp. 313–344.
Continuous and Discrete Painlevé Equations.
In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.),
NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 33–47.
… ►Now suppose that when , that is, the functions are orthogonal with respect to weighted summation on the discrete set . … ►
Example. The Discrete Fourier Transform… ►is called a discrete Fourier transform pair. … ►The direct computation of the discrete Fourier transform (3.11.38), that is, of …
… ►For an infinite set of discrete values , , of the accessory parameter , the function is analytic at , and hence also throughout the disk . …