Artículos de revistas
Monotonicity Of Zeros Of Laguerre Polynomials
Registro en:
Journal Of Computational And Applied Mathematics. , v. 233, n. 3, p. 699 - 702, 2009.
3770427
10.1016/j.cam.2009.02.038
2-s2.0-69649093907
Autor
Dimitrov D.K.
Rafaeli F.R.
Institución
Resumen
Denote by xn k (α), k = 1, ..., n, the zeros of the Laguerre polynomial Ln(α) (x). We establish monotonicity with respect to the parameter α of certain functions involving xn k (α). As a consequence we obtain sharp upper bounds for the largest zero of Ln(α) (x). © 2009 Elsevier B.V. All rights reserved. 233 3 699 702 Markov, A., Sur les racines de certaines équations (second note) (1886) Math. Ann., 27, pp. 177-182 Stieltjes, T.J., Sur les racines de l'equation Xn = 0 (1886) Acta Math., 9, pp. 385-400 G. Szego{double acute}, Orthogonal Polynomials, 4th edition, Amer. Math. Soc. Coll. Publ., 23, Providence, RI, 1975Laforgia, A., A monotonic property for the zeros of ultraspherical polynomials (1981) Proc. Amer. Math. Soc., 83, pp. 757-758 Laforgia, A., Monotonicity properties for the zeros of orthogonal polynomials and Bessel function (1985) Lecture Notes in Mathematics, 1171, pp. 267-277. , Polynomes Orthogonaux et Applications, Proceedings of the Laguerre Symposium, Bar-de-Duk, Spain, 1984, Springer-Verlag, Berlin Ismail, M.E.H., Letessier, J., Monotonicity of zeros of ultraspherical polynomials (1988) Lecture Notes in Mathematics, 1329, pp. 329-330. , Orthogonal Polynomials and Their Applications. Alfaro M., Dehesa J.S., Marcellán F.J., Rubio de Francia J.L., and Vinuesa J. (Eds), Springer-Verlag, Berlin Ismail, M.E.H., Monotonicity of zeros of orthogonal polynomials (1989) q-Series and Partitions, pp. 177-190. , Stanton D. (Ed), Springer-Verlag, New York Spigler, R., On the monotonic variation of the zeros of ultraspherical polynomials with the parameter (1984) Canad. Math. Bull., 27, pp. 472-477 Ahmed, S., Muldoon, M.E., Spigler, R., Inequalities and numerical bound for zeros of ultraspherical polynomials (1986) SIAM J. Math. Anal, 17, pp. 1000-1007 Elbert, A., Laforgia, A., A note to the paper of Ahmed Muldoon Spigler (1986) SIAM J. Math. Anal., 17, pp. 1008-1009 Ifantis, E.K., Siafarikas, P.D., Differential inequalities on the greatest zero of Laguerre and ultraspherical polynomials (1989) Actas del VI Simposium sobre Polinomios Ortogonales y Aplicaciones, pp. 187-197. , Gijon Dimitrov, D.K., On a conjecture concerning monotonicity of zeros of ultraspherical polynomials (1996) J. Approx. Theory, 85, pp. 88-97 Elbert, A., Siafarikas, P.D., Monotonicity properties of the zeros of ultraspherical polynomials (1999) J. Approx. Theory, 97, pp. 31-39 Dimitrov, D.K., Rafaeli, F.R., Monotonicity of zeros of Jacobi polynomials (2007) J. Approx. Theory, 149, pp. 15-29 Dimitrov, D.K., Rodrigues, R.O., On the behaviour of zeros of Jacobi polynomials (2002) J. Approx. Theory, 116, pp. 224-239 Calogero, F., Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomials Ln(α) (x) as the index α → ∞ and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials (1978) Nuovo Cimento, 23, pp. 101-102 Ifantis, E.K., Siafarikas, P.D., Differential inequalities and monotonicity properties of the zeros of associated Laguerre and Hermite polynomials (1995) Ann. Num. Math., 2, pp. 79-91 Natalini, P., Palumbo, B., Some monotonicity results on the zeros of the generalized Laguerre polynomials (2003) J. Comput. Appl. Math., 153, pp. 355-360 Area, I., Dimitrov, D.K., Godoy, E., Ronveaux, A., Zeros of Gegenbauer and Hermite polynomials and connection coefficients (2004) Math. Comp., 73, pp. 1937-1951 Dimitrov, D.K., Nikolov, G., Sharp bounds for the extreme zeros of classical orthogonal polynomials, , manuscript Ismail, M.E.H., Li, X., Bound on the extreme zeros of orthogonal polynomials (1992) Proc. Amer. Math. Soc., 115, pp. 131-140 Horn, R.A., Johnson, C.A., (1985) Matrix Analysis, , Cambridge Univ. Press Ismail, M.E.H., Muldoon, M.E., A discrete approach to monotonicity of zeros of orthogonal polynomials (1991) Trans. of the Amer. Math. Soc., 323, pp. 65-78 Wall, H.S., Wetzel, M., Quadratic forms and convergence regions for continued fractions (1944) Duke Math. J., 11, pp. 272-297