Differential Properties of Jacobi-Sobolev Polynomials and Electrostatic Interpretation

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dc.contributor.authorJuan Toribio-Milane
dc.contributor.authorJavier Quintero-Roba
dc.contributor.authorHΓ©ctor Pijeira-Cabrera
dc.date.accessioned2025-01-23T21:02:09Z
dc.date.available2025-01-23T21:02:09Z
dc.date.issued2023-08-06
dc.description.abstractWe study the sequence of monic polynomials {𝑆𝑛}𝑛⩾0, ortogonal with respect to the Jacobi-Sobolev inner product ⟨ 𝑓, 𝑔 βŸ©π‘  = ∫_{-1}^{1} 𝑓(π‘₯)𝑔(π‘₯)π‘‘πœ‡π›Ό,𝛽(π‘₯) + βˆ‘_{𝑗=1}^{𝑁} βˆ‘_{π‘˜=0}^{𝑑𝑗} π‘‘π‘—πœ†π‘—,π‘˜ 𝑓(π‘˜)(𝑐𝑗)𝑔(π‘˜)(𝑐𝑗), where 𝑁, 𝑑𝑗 ∈ β„€^+, πœ†π‘—,π‘˜ β©Ύ 0, π‘‘πœ‡π›Ό,𝛽(π‘₯) = (1βˆ’π‘₯)^𝛼(1+π‘₯)^𝛽𝑑π‘₯, 𝛼,𝛽 > βˆ’1, and π‘π‘—βˆˆπ‘…βˆ–(βˆ’1,1). 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}β©Ύ0 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.
dc.identifier.citationPijeira-Cabrera, H., Quintero-Roba, J., & Toribio-Milane, J. (2023). Differential properties of Jacobi-Sobolev polynomials and electrostatic interpretation. Mathematics, 11(3420).
dc.identifier.urihttps://repositoriovip.uasd.edu.do/handle/123456789/746
dc.language.isoen
dc.titleDifferential Properties of Jacobi-Sobolev Polynomials and Electrostatic Interpretation
dc.typeArticle
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