{"issue":"8","doi":"10.1112/s0010437x13007045","keyword":["Algebra and Number Theory"],"department":[{"_id":"555"}],"_id":"37672","year":"2013","citation":{"ieee":"M. Rösler, T. Koornwinder, and M. Voit, “Limit transition between hypergeometric functions of type BC and type A,” Compositio Mathematica, vol. 149, no. 8, pp. 1381–1400, 2013, doi: 10.1112/s0010437x13007045.","short":"M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.","mla":"Rösler, Margit, et al. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica, vol. 149, no. 8, Wiley, 2013, pp. 1381–400, doi:10.1112/s0010437x13007045.","chicago":"Rösler, Margit, Tom Koornwinder, and Michael Voit. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica 149, no. 8 (2013): 1381–1400. https://doi.org/10.1112/s0010437x13007045.","ama":"Rösler M, Koornwinder T, Voit M. Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica. 2013;149(8):1381-1400. doi:10.1112/s0010437x13007045","apa":"Rösler, M., Koornwinder, T., & Voit, M. (2013). Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica, 149(8), 1381–1400. https://doi.org/10.1112/s0010437x13007045","bibtex":"@article{Rösler_Koornwinder_Voit_2013, title={Limit transition between hypergeometric functions of type BC and type A}, volume={149}, DOI={10.1112/s0010437x13007045}, number={8}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit and Koornwinder, Tom and Voit, Michael}, year={2013}, pages={1381–1400} }"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-437X","1570-5846"]},"abstract":[{"text":"AbstractLet ${F}_{BC} (\\lambda , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $\\rho (k)$ of positive roots. We prove that ${F}_{BC} (\\lambda + \\rho (k), k; t)$ converges as ${k}_{1} + {k}_{2} \\rightarrow \\infty $ and ${k}_{1} / {k}_{2} \\rightarrow \\infty $ to a function of type A for $t\\in { \\mathbb{R} }^{n} $ and $\\lambda \\in { \\mathbb{C} }^{n} $. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits include limit transitions for the spherical functions of non-compact Grassmann manifolds over one of the fields $ \\mathbb{F} = \\mathbb{R} , \\mathbb{C} , \\mathbb{H} $ when the rank is fixed and the dimension tends to infinity. The limit functions turn out to be exactly the spherical functions of the corresponding infinite-dimensional Grassmann manifold in the sense of Olshanski.","lang":"eng"}],"date_created":"2023-01-20T09:37:16Z","publication":"Compositio Mathematica","intvolume":" 149","date_updated":"2023-01-24T22:15:13Z","type":"journal_article","publication_status":"published","volume":149,"publisher":"Wiley","page":"1381-1400","author":[{"full_name":"Rösler, Margit","id":"37390","first_name":"Margit","last_name":"Rösler"},{"full_name":"Koornwinder, Tom","last_name":"Koornwinder","first_name":"Tom"},{"last_name":"Voit","first_name":"Michael","full_name":"Voit, Michael"}],"status":"public","title":"Limit transition between hypergeometric functions of type BC and type A","user_id":"93826"}