…
► 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.
…

…
►It is a discrete analog of theta functions.
If both $m,n$ are positive, then $G(m,n)$ 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)).
…

H. A. Yamani and W. P. Reinhardt (1975)$L$-squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian.
Phys. Rev. A11 (4), pp. 1144–1156.

…
► The analogous orthonormality is
…
►These sets may be discrete, continuous, or a combination of both, as discussed in the following three subsections.
…
►

§1.18(v) Point Spectra and Eigenfunction Expansions

…
►The properties of $V(x)$ determine whether the spectrum, this being the set of eigenvalues of $\mathscr{H}$, is discrete, continuous, or mixed, see §1.18.
…
►However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of $\mathscr{H}$ form a discrete, normed, and complete basis for a Hilbert space.
…
►The spectrum is entirely discrete as in §1.18(v).
…
►The spectrum is entirely discrete as in §1.18(v).
…
►In the attractive case (18.35.6_4) for the discrete parts of the weight function where with $$, are also simplified:
…

Hahn class (or linear lattice class).
These are OP’s ${p}_{n}(x)$ where the role of $\frac{d}{dx}$ is played
by ${\mathrm{\Delta}}_{x}$ or ${\nabla}_{x}$ or ${\delta}_{x}$
(see §18.1(i) for the definition of these operators).
The Hahn class consists of four discrete and two continuous families.

Wilson class (or quadratic lattice class).
These are OP’s ${p}_{n}(x)={p}_{n}(\lambda (y))$ (${p}_{n}(x)$ of degree $n$ in $x$,
$\lambda (y)$ quadratic in $y$) where the role of the differentiation operator
is played by $\frac{{\mathrm{\Delta}}_{y}}{{\mathrm{\Delta}}_{y}(\lambda (y))}$ or
$\frac{{\nabla}_{y}}{{\nabla}_{y}(\lambda (y))}$ or
$\frac{{\delta}_{y}}{{\delta}_{y}(\lambda (y))}$.
The Wilson class consists of two discrete and two continuous families.

…
►The Hahn class consists of four discrete families (Hahn, Krawtchouk, Meixner, and Charlier) and two continuous families (continuous Hahn and Meixner–Pollaczek).
…
►

Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, standardizations, and parameter constraints.
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