共查询到20条相似文献,搜索用时 15 毫秒
1.
Rodica D. Costin 《Journal of Approximation Theory》2009,161(2):787-801
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a three term recurrence relation, integral inter-relations, and weak orthogonality relations. 相似文献
2.
Vladimir D. Stepanov 《Proceedings of the American Mathematical Society》2008,136(5):1589-1597
For a weight function generating the classical Jacobi polynomials, the sharp double estimate of the distance from the subspace of all polynomials of an arbitrary fixed order is established.
3.
Bidyut Guha Thakurta 《Proceedings Mathematical Sciences》1986,95(1):53-59
In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> n (a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra. 相似文献
4.
H. T. Koelink 《Proceedings of the American Mathematical Society》1996,124(3):887-898
Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform, and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula. In a special case this relation dates back to work by Bateman in 1933 and we follow a part of the historical development for these polynomials. Some applications of this relation are given.
5.
The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so-called Bernstein–Bézier form of a polynomial. 相似文献
6.
Clemens Markett 《Indagationes Mathematicae》2019,30(1):81-93
For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest classes of such eigenfunctions known so far, is given by Koornwinder’s generalized Jacobi polynomials with four parameters and determining the orthogonality measure on the interval . The corresponding differential equation of order is presented here as a linear combination of four elementary components which make the corresponding differential operator widely accessible for applications. In particular, we show that this operator is symmetric with respect to the underlying scalar product and thus verify the orthogonality of the eigenfunctions. 相似文献
7.
Abdullah Alt?n 《Journal of Mathematical Analysis and Applications》2009,353(1):121-1933
The main object of this paper is to construct a systematic investigation of a multivariable extension of the extended Jacobi polynomials and give some relations for these polynomials. We derive various families of multilinear and multilateral generating functions. We also obtain relations between the polynomials extended Jacobi polynomials and some other well-known polynomials. Other miscellaneous properties of these general families of multivariable polynomials are also discussed. Furthermore, some special cases of the results are presented in this study. 相似文献
8.
Walter Gautschi 《Numerical Algorithms》2009,50(1):93-96
Inequalities for the largest zero of Jacobi polynomials, conjectured recently by us and in joint work with P. Leopardi, are
here extended to all zeros of Jacobi polynomials, and new relevant conjectures are formulated based on extensive computation.
相似文献
9.
Stamatis Koumandos 《Numerical Algorithms》2007,44(3):249-253
Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality
holds for α,β > − 1 and n ≥ 1, θ ∈ (0, π), where are the Jacobi polynomials of degree n and parameters (α, β). We settle this conjecture in the special cases where .
相似文献
10.
11.
We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi polynomials play a key role in the proof. 相似文献
12.
《Discrete Mathematics》2023,346(6):113339
In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs. 相似文献
13.
Inequalities are conjectured for the Jacobi polynomials and their largest zeros. Special attention is given to the cases β = α − 1 and β = α.
相似文献
14.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1