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For each fixed value of $\beta$ in the range $-2

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 contiguous relations satisfied by the polynomials, to establish the quasi-orthogonality of certain $_2\phi_2$ and $_3\phi_2$ polynomials. The location and interlacing properties of the real zeros of these quasi-orthogonal polynomials are studied. Interlacing properties of the zeros of $q$-Laguerre quasi-orthogonal polynomials $L_n^{(\delta)}(z;q)$ when $-2

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 contiguous relations satisfied by the polynomials, to establish the quasi-orthogonality of certain $_2��_2$ and $_3��_2$ polynomials. The location and interlacing properties of the real zeros of these quasi-orthogonal polynomials are studied. Interlacing properties of the zeros of $q$-Laguerre quasi-orthogonal polynomials $L_n^{(��)}(z;q)$ when $-2

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 Jacobi polynomials to determine the intervals on the real line where the zeros are located.

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 $K_n(x;p,N)=(-N)_n\phantom{}_2F_1(-n,-x;-N;\frac1{p})$, $n=0,1,...N$, $0n-1$, the quasi-orthogonal polynomials $K_{n}(x;p,a)$, $k-11$ or $p

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 $\phantom{}_2F_1(a,1;c;z)$ and the remainder term $Q_{mn}(z)\phantom{}_2F_1(a,1;c;z)-P_{mn}(z)$ were explicitly evaluated by Pad\'e (cf. \cite{2}, \cite{5} or \cite{7}). We show that for $c>a>0$ and $m\geq n-1$, the poles of $P_{mn}(z)/Q_{mn}(z)$ lie on the cut $(1,\infty)$. We deduce that the sequence of approximants $P_{mn}(z)/Q_{mn}(z)$ converges to $\phantom{}_2F_1(a,1;c;z)$ as $m \to \infty$, $ n/m \to \rho$ with $0a>0$

The Pad�� 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�� approximant $P_{mn}(z)/Q_{mn}(z)$ for $\phantom{}_2F_1(a,1;c;z)$ and the remainder term $Q_{mn}(z)\phantom{}_2F_1(a,1;c;z)-P_{mn}(z)$ were explicitly evaluated by Pad�� (cf. \cite{2}, \cite{5} or \cite{7}). We show that for $c>a>0$ and $m\geq n-1$, the poles of $P_{mn}(z)/Q_{mn}(z)$ lie on the cut $(1,\infty)$. We deduce that the sequence of approximants $P_{mn}(z)/Q_{mn}(z)$ converges to $\phantom{}_2F_1(a,1;c;z)$ as $m \to \infty$, $ n/m \to ��$ with $0a>0$

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 that have been fully analyzed impose additional restrictions on $b$ and $c$. We review recent results that have been proved for the zeros of several classes of hypergeometric polynomials $F(-n,b; c; z)$ where $b$ and $c$ are real. We show that the number of real zeros of $F(-n,b; c; z)$ for arbitrary real values of the parameters $b$ and $c$, as well as the intervals in which these zeros (if any) lie, can be deduced from corresponding results for Jacobi polynomials.

N2O is known to be a greenhouse gas with a high global warming potential, approximately 296 times higher than that of CO2 [11]. In road vehicles N2O is mostly formed by reactions in the exhaust catalyst. The IPCC (Intergovernmental Panel on Climate Changes) uses emission factors from research performed in the late 1980's and early 1990's to calculate the contribution of road traffic to the global emission of N2O. however, in the last decades much has changed with respect to vehicle technology. Furthermore, the currently available N2O emission factors for Heavy Duty (HD) vehicles have been extrapolated from the Light Duty (LD) emission factors by an assumed correlation with NOx emissions. Because of the high global warming potential, a clear need existed to derive reliable emission factors for N2O that reflect the pasr, present and expected future contribution from traffic (The object period is defined as 1988 until 2010). A measuring programme of substantial size and diversity in vehicle technologies was considered far more relevant than a theoretical approach based on literature.

unavailable at this time... Mathematics Subject Classification (2000): 41A21, 30E15 Quaestiones Mathematicae 25 (2002), 539-545

We prove that the zeros of some families of F23 hypergeometric polynomials are all real and negative. This result has a connection with the theory of Pólya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity.