An Expansion Formula for the Askey-Wilson Function

@article{Stokman2002AnEF,
  title={An Expansion Formula for the Askey-Wilson Function},
  author={Jasper V. Stokman},
  journal={Journal of Approximation Theory},
  year={2002},
  volume={114},
  pages={308-342}
}
The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion formula at hand, the image under the Askey-Wilson function transform of an Askey-Wilson polynomial… CONTINUE READING

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