In terms of classical Bessel function, we represent explicitly the radial part of Whittaker functions on SU(2,1) belonging to the large discrete series representations. Moreover we compute archimedean local L-factors corresponding to a construction of L-function by Gelbart and Piatetski-Shapiro.
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Harutaka Koseki, Takayuki Oda, Whittaker Functions for the Large Discrete Series Representations of <i>SU</i>(2, 1) and Related Zeta Integrals. Publ. Res. Inst. Math. Sci. 31 (1995), no. 6, pp. 959–999DOI 10.2977/PRIMS/1195163592