electrostatic interpretation
Recently Published Documents


TOTAL DOCUMENTS

29
(FIVE YEARS 0)

H-INDEX

9
(FIVE YEARS 0)

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1250
Author(s):  
Abey S. Kelil ◽  
Appanah R. Appadu

Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical modified Freud-type polynomials in which their corresponding semi-classical weight function is a more general deformation of the classical scaled sextic Freud weight |x|αexp(−cx6),c>0,α>−1. Certain characterizing properties of these polynomials such as moments, recurrence coefficients, holonomic equations that they satisfy, and certain non-linear differential-recurrence equations satisfied by the recurrence coefficients, using compatibility conditions for ladder operators for these orthogonal polynomials, are investigated. Differential-difference equations were also obtained via Shohat’s quasi-orthogonality approach and also second-order linear ODEs (with rational coefficients) satisfied by these polynomials. Modified Freudian polynomials can also be obtained via Chihara’s symmetrization process from the generalized Airy-type polynomials. The obtained linear differential equation plays an essential role in the electrostatic interpretation for the distribution of zeros of the corresponding Freudian polynomials.



2020 ◽  
Vol 61 (5) ◽  
pp. 053501
Author(s):  
K. Castillo ◽  
M. N. de Jesus ◽  
J. Petronilho










2013 ◽  
Vol 55 (1) ◽  
pp. 39-54
Author(s):  
LUIS ALEJANDRO MOLANO MOLANO

AbstractWe study the sequence of monic polynomials orthogonal with respect to inner product $$\begin{eqnarray*}\langle p, q\rangle = \int \nolimits \nolimits_{0}^{\infty } p(x)q(x){e}^{- x} {x}^{\alpha } \hspace{0.167em} dx+ Mp(\zeta )q(\zeta )+ N{p}^{\prime } (\zeta ){q}^{\prime } (\zeta ),\end{eqnarray*}$$ where $\alpha \gt - 1$, $M\geq 0$, $N\geq 0$, $\zeta \lt 0$, 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.



Sign in / Sign up

Export Citation Format

Share Document