# Christoffel coefficients (or numbers)

♦
3 matching pages ♦

(0.001 seconds)

## 3 matching pages

##### 1: 3.5 Quadrature

…
►

3.5.18
$${w}_{k}={\int}_{a}^{b}\frac{{p}_{n}(x)}{(x-{x}_{k}){p}_{n}^{\prime}({x}_{k})}w(x)dx.$$

►The ${w}_{k}$ are also known as *Christoffel coefficients*or*Christoffel numbers*and they are all positive. The remainder is given by …##### 2: Bibliography N

…
►
Tables of Lagrangian Interpolation Coefficients.
Columbia University Press, New York.
…
►
Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors.
2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
…
►
An explicit formula for the coefficients in Laplace’s method.
Constr. Approx. 38 (3), pp. 471–487.
…
►
Géza Freud, orthogonal polynomials and Christoffel functions. A case study.
J. Approx. Theory 48 (1), pp. 3–167.
…

##### 3: Errata

…
►
Section 34.1
…
►
Section 34.1
…
►
Subsection 1.2(i)
…
►
Subsection 14.18(iii)
…
►
Equation (10.20.14)
…

The relation between Clebsch-Gordan and $\mathit{3}j$ symbols was clarified, and the sign of ${m}_{3}$ was changed for readability. The reference Condon and Shortley (1935) for the Clebsch-Gordan coefficients was replaced by Edmonds (1974) and Rotenberg et al. (1959) and the references for $\mathit{3}j$, $\mathit{6}j$, $\mathit{9}j$ symbols were made more precise in §34.1.

10.20.14
$${B}_{3}(0)=-\frac{\mathrm{959\hspace{0.33em}71711\hspace{0.33em}84603}}{\mathrm{25\hspace{0.33em}47666\hspace{0.33em}37125\hspace{0.33em}00000}}{2}^{\frac{1}{3}}$$

Originally this coefficient was given incorrectly as ${B}_{3}(0)=-\frac{\mathrm{430\hspace{0.33em}99056\hspace{0.33em}39368\hspace{0.33em}59253}}{\mathrm{5\hspace{0.33em}68167\hspace{0.33em}34399\hspace{0.33em}42500\hspace{0.33em}00000}}{2}^{\frac{1}{3}}$. The other coefficients in this equation have not been changed.

*Reported 2012-05-11 by Antony Lee.*