# continuous

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## 1—10 of 89 matching pages

##### 1: 32.16 Physical Applications

##### 2: 1.4 Calculus of One Variable

###### §1.4(ii) Continuity

… ► … ► … ►For an example, see Figure 1.4.1 … ►###### Absolutely Continuous Stieltjes Measure

…##### 3: 18.25 Wilson Class: Definitions

###### §18.25(ii) Weights and Standardizations: Continuous Cases

… ►###### Continuous Dual Hahn

… ►Table 18.25.2 provides the leading coefficients ${k}_{n}$ (§18.2(iii)) for the Wilson, continuous dual Hahn, Racah, and dual Hahn polynomials. …##### 4: About Color Map

###### Continuous Phase Mapping

►For the continuous phase mapping, we map the phase continuously onto the hue, as both are periodic. … ► …##### 5: 18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes

##### 6: 18.1 Notation

Continuous Hahn: ${p}_{n}(x;a,b,\overline{a},\overline{b})$.

Continuous Dual Hahn: ${S}_{n}(x;a,b,c)$.

Continuous $q$-Ultraspherical: ${C}_{n}(x;\beta |q)$.

Continuous $q$-Hermite: ${H}_{n}\left(x|q\right)$.

Continuous ${q}^{-1}$-Hermite: ${h}_{n}\left(x|q\right)$

##### 7: 18.26 Wilson Class: Continued

###### Wilson $\to $ Continuous Dual Hahn

… ►###### Wilson $\to $ Continuous Hahn

… ►###### Continuous Dual Hahn $\to $ Meixner–Pollaczek

… ►###### Continuous Dual Hahn

… ►Koornwinder (2009) rescales and reparametrizes Racah polynomials and Wilson polynomials in such a way that they are continuous in their four parameters, provided that these parameters are nonnegative. …##### 8: 18.28 Askey–Wilson Class

###### §18.28(v) Continuous $q$-Ultraspherical Polynomials

… ►###### §18.28(vi) Continuous $q$-Hermite Polynomials

… ►###### §18.28(ix) Continuous $q$-Jacobi Polynomials

… ►Specialization to continuous $q$-ultraspherical: … ►###### From Continuous $q$-Ultraspherical to Continuous $q$-Hermite

…##### 9: 18.19 Hahn Class: Definitions

*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.