- Title
- Effective Laguerre asymptotics
- Creator
- Borwein, David; Borwein, Jonathan M.; Crandall, Richard E.
- Relation
- SIAM Journal on Numerical Analysis Vol. 46, Issue 6, p. 3285-3312
- Publisher Link
- http://dx.doi.org/10.1137/07068031X
- Publisher
- Society for Industrial and Applied Mathematics (SIAM)
- Resource Type
- journal article
- Date
- 2008
- Description
- It is known that the generalized Laguerre polynomials can enjoy subexponential growth for large primary index. In particular, for certain fixed parameter pairs (a, z) one has the large-n asymptotic behavior Ln(−a)(−z)~C(a,z)n−a/2−1/4e2√nz. We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior. We present a fast algorithm for symbolic generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i.e., rigorous and explicit) error bounds on the general expansion. A primary tool for these developments is an “exp-arc” method giving a natural bridge between converging series and effective asymptotics.
- Subject
- Laguerre polynomials; effective asymptotic expansions; contour integrals
- Identifier
- http://hdl.handle.net/1959.13/940278
- Identifier
- uon:12986
- Identifier
- ISSN:0036-1429
- Language
- eng
- Full Text
- Reviewed
- Hits: 963
- Visitors: 1777
- Downloads: 504
Thumbnail | File | Description | Size | Format | |||
---|---|---|---|---|---|---|---|
View Details Download | ATTACHMENT01 | Publisher version (open access) | 645 KB | Adobe Acrobat PDF | View Details Download |