We consider the Sobolev inner product =@!"-"1^1f(x)g(x)(1-x^2)^@a^-^1^2dx+@!f^'(x)g^'(x)d@j(x),@a>-12, where d@j is a measure involving a Gegenbauer weight and with mass points outside the interval (-1,1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product. We obtain the asymptotics of the largest zeros of these polynomials via a Mehler-Heine type formula. These results are illustrated with some numerical experiments.
['Cleonice F. Bracciali', 'Laura Castano-Garcia', 'Juan J. Moreno-Balcázar']
Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights