Journal of Inequalities and Applications
Volume 1 (1997), Issue 3, Pages 293-299
Inequalities for Laguerre functions
Department of Mathematics, The University of Melbourne, Parkville 3052, Victoria, Australia
Received 19 June 1996
Copyright © 1997 E. R. Love. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main published inequality for Laguerre functions seems to be for Laguerre polynomials only; it is [2: 10.18(3)]:
This paper presents several inequalities for Laguerre polynomials and Laguerre functions , most of which do not seem to be in the existing literature. The corresponding inequalities for confluent hypergeometric functions are noted.
For our work on expansions in series of Laguerre functions, M.N. Hunter and I needed an inequality for when re and re is large. The only extensions of the above inequality that we could obtain had multiples of on the right hand side instead of . This paper goes on to show that this is inevitable for non-integral , in that can exceed a multiple of for every fixed if is sufficiently large.