| Abstract |
In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product < f, g > = < u(M), fg > + lambda J(i)f (alpha) J(i)g (alpha), where u(M) is the Meixner linear operator, lambda is an element of R+, j is an element of N, alpha <= 0, and J is the forward difference operator Delta or the backward difference operator del. Moreover, we derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of the second order is also given. In addition, for these polynomials, we derive a (2j + 3)-term recurrence relation. Finally, we find the Mehler-Heine type formula for the particular case alpha = 0. |
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