Bounds for the Extreme Zeros of Laguerre Polynomials
By applying well-known techniques such as the Gershgorin Circle Theorem and the Euler-Rayleigh method (the latter assisted by some computer algebra), we obtain new bounds for the extreme zeroes of the n-th Laguerre polynomial. It turns out that these bounds are competitive to some of the known best bounds.
KeywordsExtreme zeros of Laguerre polynomials Gershgorin circle theorem Euler-Rayleigh method
- 6.Gupta, D.P., Muldoon, M.E.: Inequalities for the smallest zeros of Laguerre polynomials and their \(q\)-analogues. J. Ineq. Pure Appl. Math. 8(1) (2007). Article 24Google Scholar
- 13.Van der Waerden, B.L.: Modern Algebra, vol. 1. Frederick Ungar Publishing Co., New York (1949)Google Scholar