# x-difference operators

(0.008 seconds)

## 1—10 of 75 matching pages

##### 1: 25.17 Physical Applications
This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. …
##### 2: 18.42 Software
Also included is a website (CAOP) operated by a university department. …
##### 3: 26.19 Mathematical Applications
These have applications in operations research, probability theory, and statistics. …
##### 4: Brian R. Judd
Judd’s books include Operator Techniques in Atomic Spectroscopy, published by McGraw-Hill in 1963 and reprinted by Princeton University Press in 1998, Second Quantization and Atomic Spectroscopy, published by Johns Hopkins in 1967, Topics in Atomic and Nuclear Theory (with J. …
##### 5: 13.27 Mathematical Applications
Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function. The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions. …
##### 6: 26.22 Software
Also included are websites operated by university departments and consortia, research institutions, and peer-reviewed journals. …
##### 7: 34.9 Graphical Method
The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …
##### 8: Guide to Searching the DLMF
Search queries are made up of terms, textual phrases, and math expressions, combined with Boolean operators: …
• Boolean operator:

and and or

• proximity operator:

adj, prec/n, and near/n, where n is any positive natural number.

• \$ stands for any number of alphanumeric characters (the more conventional * is reserved for the multiplication operator) …
##### 9: 18.2 General Orthogonal Polynomials
###### §18.2(ii) $x$-DifferenceOperators
If the orthogonality discrete set $X$ is $\{0,1,\dots,N\}$ or $\{0,1,2,\dots\}$, then the role of the differentiation operator $\ifrac{\mathrm{d}}{\mathrm{d}x}$ in the case of classical OP’s (§18.3) is played by $\Delta_{x}$, the forward-difference operator, or by $\nabla_{x}$, the backward-difference operator; compare §18.1(i). … If the orthogonality interval is $(-\infty,\infty)$ or $(0,\infty)$, then the role of $\ifrac{\mathrm{d}}{\mathrm{d}x}$ can be played by $\delta_{x}$, the central-difference operator in the imaginary direction (§18.1(i)). …