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We investigate algebraic and analytic properties of sequences of polynomials orthogonal with respect to the Sobolev type inner product polynomials. When the values M k,i are nonnegative real numbers, we can deduce the coefficients of the recurrence relation in terms of the connection coefficients for the sequences of polynomials orthogonal with respect to the Sobolev type inner product and those orthogonal with respect to the measure μ. The matrix of a symmetric multiplication operator in terms of the above sequence of Sobolev type orthogonal polynomials is obtained from the Jacobi matrix associated with the measure μ. Finally, we focus our attention on some outer relative asymptotics of such polynomials, which are deduced by using the above connection formulas.

Orthogonal polynomials Laguerre polynomials Asymptotics Diagonal Christoffel-Darboux kernels Sobolev-type orthogonal polynomialsThe aim of this paper is to present some new results about the asymptotic behavior of the partial derivatives of the kernel polynomials associated with the Gamma distribution. We also show how these results can be used in order to obtain the inner relative asymptotics for certain Laguerre-Sobolev type polynomials.

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