Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights
نویسندگان
چکیده
Let R −∞,∞ , and let Q ∈ C2 : R → 0,∞ be an even function. In this paper, we consider the exponential-type weights wρ x |x| exp −Q x , ρ > −1/2, x ∈ R, and the orthonormal polynomials pn w2 ρ;x of degree n with respect to wρ x . So, we obtain a certain differential equation of higher order with respect to pn w2 ρ;x and we estimate the higher-order derivatives of pn w2 ρ;x and the coefficients of the higher-order Hermite-Fejér interpolation polynomial based at the zeros of pn w2 ρ;x .
منابع مشابه
Higher order Hermite-Fejér interpolation polynomials with Laguerre-type weights
* Correspondence: hsun90@skku. edu Department of Mathematics Education, Sungkyunkwan University Seoul 110-745, Republic of Korea Full list of author information is available at the end of the article Abstract Let R = [0, ∞) and R : R ® R be a continuous function which is the Laguerretype exponent, and pn, r(x), ρ > − 2 be the orthonormal polynomials with the weight wr(x) = x r e. For the zeros ...
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