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Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function
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abstract
Laurent polynomials related to the Hahn-Exton $q$-Bessel function, which are $q$-analogues 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 orthogonal polynomials the orthogonality measure is determined using the three-term recurrence relation as a starting point. The relation between Chebyshev polynomials of the second kind and the Laurent $q$-Lommel polynomials and related functions is used to obtain estimates for the latter.
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Cited by 1 Pith paper
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The $q$-extension of iterated integrals and nested sums in quantum field theory
The authors define q-extended versions of the iterated integrals and nested sums used in QFT, deriving closed forms for simple cases and algorithmic recipes for complex ones.
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