Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0729.33006
Wilson, James A.
Asymptotics for the ${}\sb 4F\sb 3$ polynomials. (English)
[J] J. Approximation Theory 66, No.1, 58-71 (1991). ISSN 0021-9045

About 15 years ago, Wilson showed that the 6-j symbols of angular momentum theory could be transformed into a set of polynomials orthogonal with respect to a measure on a finite set of points. For different choices of the parameters in these orthogonal polynomials the orthogonality is on $[0,\infty)$ with respect to a positive absolutely continuous measure, or such a measure plus a finite number of discrete masses for x negative. The absolutely continuous part of the measure decays like $\exp [-kx\sp{1/2}]$. Here the asymptotics of the polynomials is found. Regular oscillations occur, but they are stretched out by replacing n by ln n, unlike the n which occurs for Jacobi polynomials (on a finite interval), or $n\sp{1/2}$ for Laguerre polynomials (on $[0,\infty)$ but the weight function decays like exp(-x)). This interesting and important result is first found by giving different representations for these polynomials and then using a nice convexity argument. The asymptotic formula is then used to obtain an equiconvergence theorem with respect to a Dirichlet series. Finally, q- versions of these results are obtained.
[R.Askey (Madison)]

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
42A10 Trigonometric approximation

Keywords: Wilson polynomials; asymptotics; equiconvergence theorem

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]