Jung, H. S.; Sakai, R. Orthonormal polynomials with exponential-type weights. (English) Zbl 1152.41001 J. Approx. Theory 152, No. 2, 215-238 (2008). Authors’ abstract: Let \(\mathbb{R}=(-\infty,\infty)\) and let \(w_\rho (x):=| x| ^\rho \exp(-Q(x))\), where \(\rho>-\frac 12\) and \(Q(x)\in C^2: \mathbb{R}\rightarrow \mathbb{R}^+ =[0, \infty)\) is an even function. In this paper we consider the properties of the orthonormal polynomials with respect to the weight \(w^2_\rho(x)\), obtaining bounds on the orthonormal polynomials and spacing on their zeros. Moreover, we estimate \(A_n(x)\) and \(B_n(x)\) defined in Section 4, which are used in representing the derivative of the orthonormal polynomials with respect to the weight \(w^2_\rho(x)\). Reviewer: Shun Sheng Guo (Shijiazhuang) Cited in 12 Documents MSC: 41A10 Approximation by polynomials 41A27 Inverse theorems in approximation theory Keywords:Exponential weight; Orthonormal polynomials; Zeros PDFBibTeX XMLCite \textit{H. S. Jung} and \textit{R. Sakai}, J. Approx. Theory 152, No. 2, 215--238 (2008; Zbl 1152.41001) Full Text: DOI References: [1] Jung, H. S.; Sakai, R., Inequalities with exponential weights, J. Comput. Appl. Math., 212, 2, 359-373 (2008) · Zbl 1198.41001 [2] Kasuga, T.; Sakai, R., Orthonormal polynomials for generalized Freud-type weights, J. Approx. Theory, 121, 13-53 (2003) · Zbl 1034.42021 [3] Levin, A. L.; Lubinsky, D. S., Orthogonal Polynomials for Exponential Weights (2001), Springer: Springer New York · Zbl 0924.33004 [4] Levin, A. L.; Lubinsky, D. S., Orthogonal polynomials for exponential weights \(x^{2 \rho} e^{- 2 Q(x)}\) on \([0, d)\), J. Approx. Theory, 134, 199-256 (2005) · Zbl 1079.42017 [5] Levin, A. L.; Lubinsky, D. S., Orthogonal polynomials for exponential weights \(x^{2 \rho} e^{- 2 Q(x)}\) on \([0, d), II\), J. Approx. Theory, 139, 107-143 (2006) · Zbl 1127.42023 [6] G. Szegő, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, vol. 23, American Mathematical Society, Providence, RI, 1975.; G. Szegő, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, vol. 23, American Mathematical Society, Providence, RI, 1975. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.