Lifting q-difference operators for Askey-Wilson polynomials and their weight function
- Universidad Autonoma del Estado de Morelos, Facultad de Ciencias (Mexico)
We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H{sub n}(x | q) of Rogers into the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form {epsilon}{sub q}(c{sub q}D{sub q}) (where c{sub q} are some constants), defined as Exton's q-exponential function {epsilon}{sub q}(z) in terms of the Askey-Wilson divided q-difference operator D{sub q}. We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH{sub n}(x | q) up to the weight function, associated with the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q).
- OSTI ID:
- 22043912
- Journal Information:
- Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 6 Vol. 74; ISSN 1063-7788; ISSN PANUEO
- Country of Publication:
- United States
- Language:
- English
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