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On the differential equation for the Sobolev-Laguerre polynomials
Clemens Markett
The Sobolev-Laguerre polynomials form an orthogonal polynomial system with respect to a Sobolev-type inner product associated with the Laguerre measure on the positive half-axis an…
On the higher-order differential equations for the generalized Laguerre polynomials and Bessel functions
Clemens Markett
In the enduring, fruitful research on spectral differential equations with polynomial eigenfunctions, Koornwinder's generalized Laguerre polynomials are playing a prominent role. B…
An elementary representation of the higher-order Jacobi-type differential equation
Clemens Markett
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval with respect to the classical Jacobi measure and an additiona…
The higher-order differential operator for the generalized Jacobi polynomials - new representation and symmetry
Clemens Markett
For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest class…