Effective Laguerre asymptotics

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 L_n^(−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
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