We investigate weighted L p mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions. 1. Introduction. In this paper, we study weighted L p (0 < p < ∞) mean con

We study the Hankel determinant of the generalized Jacobi weight (x − t)x(1 − x) for x ∈ [0, 1] with α, β > 0, t < 0 and γ ∈ R. Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of Hankel determinant is characterized by a τ -function for the Painlevé VI system.

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods−Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov-Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before. PACS: 03.65.-w; 02.30.Gp; 03.65.Ge; 68.49.-h; 24.10.Ht

The fractional integrals involving a number of special functions and polynomials have significant importance applications in diverse areas science; for example, statistics, applied mathematics, physics, engineering. In this paper, we aim to introduce slightly modified matrix Riemann–Liouville investigate associated with products certain elementary generalized Bessel polynomials. We also conside...

In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division polynomials, we show recursive formulas for ...

We prove that transplantations for Jacobi polynomials can be derived from representation of a special integral operator as fractional Weyl’s integral. Furthermore, we show that, in a sense, Jacobi transplantation can be reduced to transplantations for ultraspherical polynomials. As an application of these results, we obtain transplantation theorems for Jacobi polynomials in ReH1 and BMO. The pa...

The DoCarmo-Wallach theory studies isometric minimal immersions f : G/K → S of a compact Riemannian homogeneous space G/K into Euclidean n -spheres for various n . For a given domain G/K , the moduli space of such immersions is a compact convex body in a representation space for the Lie group G . In 1971 DoCarmo and Wallach gave a lower bound for the (dimension of the) moduli for G/K = S , and ...