PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 64(78), pp. 53--68 (1998)
ORTHOGONAL POLYNOMIALS ON THE RADIAL RAYS AND AN ELECTROSTATIC INTERPRETATION OF ZEROS
Gradimir Milovanovi\'cKatedra za matematiku, Elektronski fakultet 18000 Ni\v s, Yugoslavia
Abstract: For polynomials orthogonal on the radial rays in the complex plane, which were introduced in , we give first a short account, and then we develop two interesting classes of orthogonal polynomials: (1) the generalized Hermite polynomials; (2) the generalized Gegenbauer polynomials. For such polynomials we obtain the corresponding linear differential equations of the second order. Assuming a logarithmic potential, we give an electrostatic interpretation of the zeros of the generalized Gegenbauer polynomials.
Classification (MSC2000): 33C45, 78A30
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