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q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations
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abstract
The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ${}_1\psi_1$-summation we complement the orthogonal q-Laguerre polynomials into an explicit orthogonal basis for the corresponding L^2-space. The dual orthogonal system consists of so-called big q-Bessel functions, which can be obtained as a rigorous limit of the orthogonal system of big q-Jacobi polynomials. Interpretations on the SU(1,1) and E(2) quantum groups are discussed.
Forward citations
Cited by 2 Pith papers
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The von Neumann algebraic quantum group $\mathrm{SU}_q(1,1)\rtimes \mathbb{Z}_2$ and the DSSYK model
The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
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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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