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1: 20.11 Generalizations and Analogs
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)). …
2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
The analogous orthonormality is … The analogs of (1.18.49)–(1.18.52) may be written in a similar fashion each now including contributions from both the discrete and continuous parts of the spectrum, as in (1.18.65). …
3: 18.39 Applications in the Physical Sciences
However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of 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). … Analogous to (18.39.7) the 3D Schrödinger operator is … Analogous to (18.39.8) the 3D time-independent Schrödinger equation with potential V ( r ) is …