Activity: Talk or presentation › Talk at workshop, seminar or course › Science to science
Description
I discuss integrals of the form
\begin{equation*}
\int_{-1}^1(C_n^{(\lambda)}(x))^2(1-x)^\alpha (1+x)^\beta\dd x,
\end{equation*}
where $C_n^{(\lambda)}$ denotes the Gegenbauer-polynomial of index $\lambda>0$ and $\alpha,\beta>-1$. Such integrals for orthogonal polynomials involving, in particular, a ``wrong'' weight function appear in physics applications and point distribution problems.
I present exact formulas for the integrals and their generating functions, and give asymptotic formulas as $n\to\infty$.
This is joint work with Peter Grabner also from TU Graz. A preprint of our paper can be found on arXiv.