Zobrazeno 1 - 10
of 110
pro vyhledávání: '"Santos, Roberto S."'
In this survey we summarize the current state of known orthogonality relations for the $q$ and $q^{-1}$-symmetric and dual subfamilies of the Askey--Wilson polynomials in the $q$-Askey scheme. These polynomials are the continuous dual $q$ and $q^{-1}
Externí odkaz:
http://arxiv.org/abs/2411.09040
Autor:
Costas-Santos, Roberto S.
Publikováno v:
Mathematics 12, no. 14 (2024), 2767
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete-continuous Sobolev-type inner product defined in terms of the Jacobi measure.
Comment: 11 pages, 2 figures
Comment: 11 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2409.04502
Publikováno v:
Rocky Mountain Journal of Mathematics 54, no. 4 (2024), 995-1004
We derive a useful result about the zeros of the $k$-polar polynomials on the unit circle; in particular we obtain a ring shaped region containing all the zeros of these polynomials. Some examples are presented.
Comment: 11 pages, 4 figures, 2 t
Comment: 11 pages, 4 figures, 2 t
Externí odkaz:
http://arxiv.org/abs/2409.00156
Autor:
Costas-Santos, Roberto S.
This contribution aims to obtain several connection formulae for the polynomial sequence, which is orthogonal with respect to the discrete Sobolev inner product \[ \langle f, g\rangle_n=\langle {\bf u}, fg\rangle+ \sum_{j=1}^M \mu_{j} f^{(\nu_j)}(c_j
Externí odkaz:
http://arxiv.org/abs/2310.12312
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to as Jacobi
Externí odkaz:
http://arxiv.org/abs/2308.13652
The big $-1$ Jacobi polynomials $(Q_n^{(0)}(x;\alpha,\beta,c))_n$ have been classically defined for $\alpha,\beta\in(-1,\infty)$, $c\in(-1,1)$. We extend this family so that wider sets of parameters are allowed, i.e., they are non-standard. Assuming
Externí odkaz:
http://arxiv.org/abs/2308.13583
We derive double product representations of nonterminating basic hypergeometric series using diagonalization, a method introduced by Theo William Chaundy in 1943. We also present some generating functions that arise from it in the $q$ and $q$-inverse
Externí odkaz:
http://arxiv.org/abs/2307.04884
In this paper we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the first and second kind. In connection with these addition theorems, we perform a full analysis of the relation between symme
Externí odkaz:
http://arxiv.org/abs/2306.03035
We study special values for the continuous $q$-Jacobi polynomials and present applications of these special values which arise from bilinear generating functions, and in particular the Poisson kernel for these polynomials.
Externí odkaz:
http://arxiv.org/abs/2303.13680
In many cases one may encounter an integral which is of $q$-Mellin--Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting $q$-Mel
Externí odkaz:
http://arxiv.org/abs/2206.05222