q-Askey scheme

♦ 1—10 of 31 matching pages ♦

(0.000 seconds)

1—10 of 31 matching pages

1: 1.11 Zeros of Polynomials

… ►

Horner’s Scheme

… ►

Extended Horner Scheme

…

2: 7.22 Methods of Computation

… ►The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing

\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(x\right)

. …

3: 37.19 Other Orthogonal Polynomials of $d$ Variables

… ► … ►Just as the classical OPs fit into the Askey scheme (see §18.19 and Figure 18.21.1) with Wilson and Racah polynomials on top, the Jacobi polynomials on the simplex fit into a scheme of OPs defined as products of one-variable OPs belonging to the Askey scheme by formulas somewhat resembling (37.14.7). However, when the one-variable OPs are taken from a higher level in the Askey scheme, the analogues of the denominators in the arguments in (37.14.7) will be parameters depending on

x_{\ell}

variables. … ►Starting from OPs in the

q

-Askey scheme (see §18.27(i)), similar constructions of

d

-variable OPs can be made. …

4: 8.25 Methods of Computation

… ►Stable recursive schemes for the computation of

E_{p}\left(x\right)

are described in Miller (1960) for

x>0

and integer

p

. …

5: 16.24 Physical Applications

… ►The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner

\mathit{6j}

symbols. …

6: Richard A. Askey

… ►Published in 1985 in the Memoirs of the American Mathematical Society, it also introduced the directed graph of hypergeometric orthogonal polynomials commonly known as the Askey scheme. …

7: 6.20 Approximations

… ►

•

Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric $U$ -function (§13.2(i)) from which Chebyshev expansions near infinity for $E_{1}\left(z\right)$ , $\mathrm{f}\left(z\right)$ , and $\mathrm{g}\left(z\right)$ follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the $U$ functions. If $|\operatorname{ph}z|<\pi$ the scheme can be used in backward direction.

…