论文信息 - Bounds for zeros of the Laguerre polynomials - 字舞流文

Bounds for zeros of the Laguerre polynomials

We establish new inequalities on the extreme zeros of the Laguerre polynomials which are uniform in all the parameters involved.

[1] J. Jensen,et al. Recherches sur la théorie des équations , 1913 .

[2] Ilia Krasikov,et al. Nonnegative Quadratic Forms and Bounds on Orthogonal Polynomials , 2001, J. Approx. Theory.

[3] Ilia Krasikov,et al. EXPLICIT BOUNDS FOR HERMITE POLYNOMIALS IN THE OSCILLATORY REGION , 2000 .

[4] Merrell L. Patrick,et al. Extensions of inequalities of the Laguerre and Turán type , 1973 .

[5] Merrell L. Patrick. Some Inequalities Concerning Jacobi Polynomials , 1971 .

[6] Xin Li,et al. Bound on the extreme zeros of orthogonal polynomials , 1992 .

[7] Karl Dilcher,et al. On a class of nonlinear differ-ential operators acting on polynomials , 1992 .

[8] W. J. Studden,et al. Some new asymptotic properties for the zeros of Jacobi, Laguerre, and Hermite polynomials , 1994, math/9406224.

[9] Wolfgang Gawronski. STRONG ASYMPTOTICS AND THE ASYMPTOTIC ZERO DISTRIBUTIONS OF LAGUERRE POLYNOMIALS Ln(an+α) AND HERMITE POLYNOMIALS Ηn(an+α) , 1993 .

[10] Mourad E. H. Ismail,et al. On asymptotics of Jacobi polynomials , 1991 .