Monotonicity of zeros of Jacobi¿Sobolev type orthogonal polynomials

• Autores: Dimitar K. Dimitrov, Mirela V. Mello, Fernando R. Rafaeli
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 3, 2010, págs. 263-276
• Idioma: inglés
• DOI: 10.1016/j.apnum.2009.12.004
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• Resumen

  • Consider the inner product View the MathML source where ?,?>-1 and View the MathML source. If View the MathML source, we denote by View the MathML source, k=1,�,n, the zeros of the n-th polynomial View the MathML source, orthogonal with respect to the above inner product. We investigate the location, interlacing properties, asymptotics and monotonicity of View the MathML source with respect to the parameters View the MathML source in two important cases, when either View the MathML source or View the MathML source. The results are obtained through careful analysis of the behavior and the asymptotics of the zeros of polynomials of the form pn(x)=hn(x)+cgn(x) as functions of c.