论文信息 - An upper bound on Jacobi polynomials

An upper bound on Jacobi polynomials

Let P"k^(^@a^,^@b^)(x) be an orthonormal Jacobi polynomial of degree k. We will establish the following inequality:[email protected]?[@d"-"1,@d"1]([email protected]"-"1)(@d"1-x)(1-x)^@a(1+x)^@bP"k^(^@a^,^@b^)(x)^2 =6,@a>[email protected]>=1+24.

Ilia Krasikov

[1] R. Sakai,et al. Orthonormal polynomials with generalized Freud-type weights , 2003, J. Approx. Theory.

[2] Yunshyong Chow,et al. A Bernstein-type inequality for the Jacobi polynomial , 1994 .

[3] Tamás Erdélyi,et al. Generalized Jacobi Weights, Christoffel Functions, and Jacobi-polynomials (vol 25, Pg 602, 1994) , 1994 .

[4] Doron S. Lubinsky,et al. Orthogonal Polynomials for Exponential Weights , 2001 .

[5] Doron S. Lubinsky,et al. Orthogonal polynomials for exponential weights x2rhoe-2Q(x) on [0, d) , 2005, J. Approx. Theory.

[6] Tamás Erdélyi,et al. Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials , 1994 .

[7] Ilia Krasikov. On the Erdelyi-Magnus-Nevai Conjecture for Jacobi Polynomials , 2008 .

[8] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[9] L. J. Landau,et al. Bessel Functions: Monotonicity and Bounds , 2000 .

[10] Ilia Krasikov. On the maximum value of Jacobi polynomials , 2005, J. Approx. Theory.

[11] L. Lorch. Inequalities for ultraspherical polynomials and the gamma function , 1984 .

[12] Ilia Krasikov,et al. Inequalities for orthonormal Laguerre polynomials , 2007, J. Approx. Theory.