Upper bounds on generalized Laguerre polynomials - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T15:18:33Z http://mathoverflow.net/feeds/question/85005 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85005/upper-bounds-on-generalized-laguerre-polynomials Upper bounds on generalized Laguerre polynomials Alex Gittens 2012-01-05T22:03:09Z 2012-02-04T12:13:58Z <p>I evaluated an integral and obtained an expression with a Laguerre polynomial. I'd like something more explicit and useable.</p> <p>Are there any known simple (e.g. exponential) upper bounds on the generalized Laguerre polynomials $L_{n}^{(\alpha)}(x)$? </p> <p>So far I've only found some asymptotic expansions, but I'd like an actual upper bound.</p> http://mathoverflow.net/questions/85005/upper-bounds-on-generalized-laguerre-polynomials/87521#87521 Answer by Andrei MF for Upper bounds on generalized Laguerre polynomials Andrei MF 2012-02-04T12:13:58Z 2012-02-04T12:13:58Z <p>What kind of estimates exactly do you need? It is difficult to help if you are not more specific. At any rate, I believe there are many references you could check. You might find some useful inequalities in the papers:</p> <p>1) "A Sharp Inequality of Markov Type for Polynomials Associated with Laguerre Weight" by Holly Carley, Xin Li, and R N. Mohapatra, Journal of Approximation Theory 113 (2001) 221–228</p> <p>2) "Some inequalities for algebraic polynomials with the Laguerre weight" by Semyon Rafalson, Journal of Approximation Theory 143 (2006) 201 – 218</p> <p>3) "Inequalities for orthonormal Laguerre polynomials" by Ilia Krasikov, Journal of Approximation Theory 144 (2007) 1 – 26 (see the references therein)</p> <p>Last but not least, check the NIST Digital Library of Mathematical Functions online at <a href="http://dlmf.nist.gov/" rel="nofollow">http://dlmf.nist.gov/</a>, in particular, <a href="http://dlmf.nist.gov/18.14" rel="nofollow">http://dlmf.nist.gov/18.14</a></p>