A Combinatorial Interpretation of Lommel Polynomials and Their Derivatives
نویسندگان
چکیده
In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis.
منابع مشابه
. C A ] 1 4 Fe b 19 95 ORTHOGONAL POLYNOMIALS AND LAURENT POLYNOMIALS RELATED TO THE HAHN - EXTON q - BESSEL FUNCTION
Laurent polynomials related to the Hahn-Exton q-Bessel function, which are qanalogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurent q-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orth...
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تاریخ انتشار 2015