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ON LAGUERRE–SOBOLEV TYPE ORTHOGONAL POLYNOMIALS: ZEROS AND ELECTROSTATIC INTERPRETATION
Published online by Cambridge University Press: 08 October 2013
Abstract
We study the sequence of monic polynomials orthogonal with respect to inner product $$\begin{eqnarray*}\langle p, q\rangle = \int \nolimits \nolimits_{0}^{\infty } p(x)q(x){e}^{- x} {x}^{\alpha } \hspace{0.167em} dx+ Mp(\zeta )q(\zeta )+ N{p}^{\prime } (\zeta ){q}^{\prime } (\zeta ),\end{eqnarray*}$$
$\alpha \gt - 1$,
$M\geq 0$,
$N\geq 0$,
$\zeta \lt 0$, and
$p$ and
$q$ are polynomials with real coefficients. We deduce some interlacing properties of their zeros and, by using standard methods, we find a second-order linear differential equation satisfied by the polynomials and discuss an electrostatic model of their zeros.
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- Research Article
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- Copyright
- Copyright ©2013 Australian Mathematical Society
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