Convolutions for orthogonal polynomials from Lie and quantum algebra representations.

  title={Convolutions for orthogonal polynomials from Lie and quantum algebra representations.},
  author={H. T. Koelink and Joris Van der Jeugt},
  journal={Siam Journal on Mathematical Analysis},
Theinterpretation of the Meixner--Pollaczek, Meixner, and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra ${\frak{su}}(1,1)$ and the Clebsch--Gordan decomposition lead to generalizations of the convolution identities for these polynomials. Using the Racah coefficients, convolution identities for continuous Hahn, Hahn, and Jacobi polynomials are obtained. From the quantized universal enveloping algebra for ${\frak{su}}(1,1… 
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