Double summation addition theorems for Jacobi functions of the first and second kind
Cohl, H. S., Costas-Santos R.S., Durand, L., Montoya C. and Ólafsson, G. Contemporary Mathematics 818, Classical Hypergeometric Functions and Generalizations, Amer. Math. Soc., Providence, RI, Eds: Howard S. Cohl, Roberto S. Costas-Santos and Robert S. Maier, 25—70, 2025Abstract
We study special values for the continuous \(q\)-Jacobi polynomials and present applications of these special values, which arise from bilinear generating functions and, in particular, the Poisson kernel for these polynomials.
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BibTeX
@incollection {MR4901158,
AUTHOR={Cohl, H. S. and Costas-Santos, R. S. and Durand, L. and Montoya, C. and \'{O}lafsson, G.},
TITLE={Double summation addition theorems for {J}acobi functions of the first and second kind},
BOOKTITLE={Classical hypergeometric functions and generalizations},
SERIES={Contemp. Math.},
VOLUME={818},
PAGES={25--70},
PUBLISHER={Amer. Math. Soc., [Providence], RI},
YEAR={[2025] \copyright 2025},
MRCLASS={54C40 (33C45)},
MRNUMBER={4901158},
DOI={10.1090/conm/818/16367},
URL={https://doi.org/10.1090/conm/818/16367},
}