Geodesic
Generating functions of Chebyshev polynomials in three variables
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 246-259

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In this paper generating functions of three-variable Chebyshev polynomials (of the first, as well as of the second type) associated with the root system of $A_3$ Lie algebra are obtained. 
@article{ZNSL_2015_433_a12,
     author = {M. A. Sokolov},
     title = {Generating functions of {Chebyshev} polynomials in three variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {246--259},
     publisher = {mathdoc},
     volume = {433},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a12/}
}
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M. A. Sokolov. Generating functions of Chebyshev polynomials in three variables. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 246-259. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a12/