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# Talk: Krawtchuk Sobolev polynomials. Old and new results

Krawtchuk Sobolev polynomials. Old and new results

Date: 2006..06..02
Event: International congress COMPUMATG 2022
In this talk we present different connection formulas for the Krawtchuk Sobolev polynomials which are orthogonal with respect to the inner product: $(f,g)_S = \langle {\bf u}, fg \rangle + \lambda \Delta^i f(c)\Delta^i g(c),$ where $${\bf u}$$ is the lineal form associated to the Krawtchuk polynomials, $$i$$ is a positive integer, $$\lambda, c$$ are real numbers, and $$\Delta$$ is the forward difference operator.
We will also show an holonomic second order difference equation that this succession of polynomials satisfies as well as a factorisation of this family of polynomials for $$n\ge N$$ through which we can define a new internal product with respect to which the sequence of Krawtchuk Sobolev polynomials are orthogonal for degrees higher than $$N$$.