Differential Properties of Jacobi –Sobolev Polynomials and electrostatic Interpretation
Differential Properties of Jacobi –Sobolev Polynomials and electrostatic Interpretation
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Date
2023/08/05
Authors
Juan Toribio Milane
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Abstract
A connection formula that relates the Sobolev polynomials 𝑆𝑛
with the Jacobi polynomials is provided, as well as the ladder differential operators for the sequence {𝑆𝑛}𝑛⩾0
and a second-order differential equation with a polynomial coefficient that they satisfied. We give sufficient conditions under which the zeros of a wide class of Jacobi-Sobolev polynomials can be interpreted as the solution of an electrostatic equilibrium problem of n unit charges moving in the presence of a logarithmic potential. Several examples are presented to illustrate this interpretation.
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Milane, J. T. (2023). Differential Properties of Jacobi–Sobolev Polynomials and electrostatic Interpretation. Mathematics, 11(15), 3420.