Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 117-120 (2001)

Discrete Laguerre functions and equilibrium conditions

Ferenc Schipp

Department of Numerical Analysis, Eötvös L. University; Computer and Automation Research Institute of HAS, University of Pécs, Pázmány Péter sétány I/D, H-1117 Budapest, HUNGARY

Abstract: The discrete Laguerre functions $L_n^a (n\in\Bbb N)$ forms an orthonormal system on the unite circle $\Bbb T$ and the finite set of functions $L_n^a (n=0,1,\cdots, N-1)$ is orthonormal with respect to a discrete scalar product defined by the discrete subset $\Bbb T_N^a$ of $\Bbb T$. It is showed that the set $\Bbb T_N^a$ can be interpreted as a solution of an electrostatic equilibrium problem.

Keywords: Discrete Laguerre system, discrete orthogonal systems, electrostatic equilibrium.

Classification (MSC2000): 42C05; 33C52

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