Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Jordaan K"'
Autor:
Jooste, AS, Jordaan, K.
In this paper we consider connection formulae for orthogonal polynomials in the context of Christoffel transformations for the case where a weight function, not necessarily even, is multiplied by an even function $c_{2k}(x),k\in \mathbb{N}_0$. When $
Externí odkaz:
http://arxiv.org/abs/2312.09931
Autor:
Jooste, A. S., Jordaan, K.
For each fixed value of $\beta$ in the range $-2<\beta<-1$ and $0
Externí odkaz:
http://arxiv.org/abs/2302.04193
We state and prove the $q$-extension of a result due to Johnston and Jordaan (cf. \cite{Johnston-2015}) and make use of this result, the orthogonality of $q$-Laguerre, little $q$-Jacobi, $q$-Meixner and Al-Salam-Carlitz I polynomials as well as conti
Externí odkaz:
http://arxiv.org/abs/1912.00353
Publikováno v:
In Journal of Computational and Applied Mathematics 15 October 2020 377
We use a method based on the division algorithm to determine all the values of the real parameters $b$ and $c$ for which the hypergeometric polynomials $_2F_1(-n, b; c; z)$ have $n$ real, simple zeros. Furthermore, we use the quasi-orthogonality of J
Externí odkaz:
http://arxiv.org/abs/1301.4771
Autor:
Driver, K., Jordaan, K.
We derive upper bounds for the smallest zero and lower bounds for the largest zero of Laguerre, Jacobi and Gegenbauer polynomials. Our approach uses mixed three term recurrence relations satisfied by polynomials corresponding to different parameter(s
Externí odkaz:
http://arxiv.org/abs/1111.1218
We investigate the zeros of a family of hypergeometric polynomials $_2F_1(-n,-x;a;t)$, $n\in\nn$ that are known as the Meixner polynomials for certain values of the parameters $a$ and $t$. When $a=-N$, $N\in\nn$ and $t=\frac1{p}$, the polynomials $K_
Externí odkaz:
http://arxiv.org/abs/0901.0817
Autor:
Driver, K, Jordaan, K
Publikováno v:
Quaestiones Mathematicae, 25 (2002), 1-7
The Pad\'e table of $\phantom{}_2F_1(a,1;c;z)$ is normal for $c>a>0$ (cf. \cite{3}). For $m \geq n-1$ and $c \notin {\zz}^{\phantom{}^-}$, the denominator polynomial $Q_{mn}(z)$ in the $[m/n]$ Pad\'e approximant $P_{mn}(z)/Q_{mn}(z)$ for $\phantom{}_
Externí odkaz:
http://arxiv.org/abs/0901.0435
Autor:
Driver, K, Jordaan, K
Publikováno v:
Algorithms for Approximation IV, Proceedings of the 2001 International Symposium: 436-445
Our interest lies in describing the zero behaviour of Gauss hypergeometric polynomials $F(-n,b; c; z)$ where $b$ and $c$ are arbitrary parameters. In general, this problem has not been solved and even when $b$ and $c$ are both real, the only cases th
Externí odkaz:
http://arxiv.org/abs/0812.0708
Autor:
Jordaan, K, Tookos, F
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as function
Externí odkaz:
http://arxiv.org/abs/0812.0726