Results 101 to 110 of about 122,453 (243)

Cariñena polynomials are Jacobi polynomials [PDF]

arXiv, 2009
We show that the Cari\~{n}ena orthogonal polynomials are Jacobi polynomials; moreover, there exists a natural bijection between the negative and the positive curvature cases. These results hold only in the two dimensional case.
arxiv  

Hankel determinants and Jacobi continued fractions for $q$-Euler numbers

Comptes Rendus. Mathématique
The $q$-analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the $q$-Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the $q$-Euler ...
Chern, Shane, Jiu, Lin
doaj   +1 more source

The Zeros of Orthogonal Polynomials for Jacobi-Exponential Weights

Abstract and Applied Analysis, 2012
This paper gives the estimates of the zeros of orthogonal polynomials for Jacobi-exponential weights.
Rong Liu, Ying Guang Shi
doaj   +1 more source

Jacob's ladders and new orthogonal systems generated by Jacobi polynomials [PDF]

arXiv, 2010
Is is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the classical Jacobi's polynomials, i.e.
arxiv  

Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

, 2004
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials.
Derriennic, Marie-Madeleine
core   +3 more sources

A Bochner Theorem for Dunkl Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions.
Luc Vinet, Alexei Zhedanov
doaj   +1 more source

Generating functions of Jacobi and related polynomials [PDF]

, 1951
Fred Brafman
openalex   +1 more source

Coupling coefficients of suq(1,1) and multivariate q-Racah polynomials

Nuclear Physics B, 2018
Gasper & Rahman's multivariate q-Racah polynomials are shown to arise as connection coefficients between families of multivariate q-Hahn or q-Jacobi polynomials. The families of q-Hahn polynomials are constructed as nested Clebsch–Gordan coefficients
Vincent X. Genest, Plamen Iliev, Luc Vinet   +2 more
doaj   +1 more source

On the zeros of certain polynomials related to Jacobi and Laguerre polynomials [PDF]

, 1932
Wayne Lawton
openalex   +1 more source

On the maximum value of Jacobi polynomials

Journal of Approximation Theory, 2005
AbstractA remarkable inequality, with utterly explicit constants, established by Erdélyi, Magnus, and Nevai, states that for α⩾β>-12, the orthonormal Jacobi polynomials Pk(α,β)(x) satisfymax|x|⩽1(1-x)α+1/2(1+x)β+1/2Pk(α,β)(x)2=O(α)[Erdélyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal.
openaire   +2 more sources