Ol’shanskij, G. I. Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities. (English. Russian original) Zbl 1075.43009 Funct. Anal. Appl. 37, No. 4, 281-301 (2003); translation from Funks. Anal. Prilozh. 37, No. 4, 49-73 (2003). The author presents several proofs of some combinatorial identities which may be regarded as multidimensional analogs of Dougall’s formula for bilateral hypergeometric series. The main proof uses representations of series of classical compact symmetric spaces which finally leads to these identities for discrete parameters. The general case is the obtained via analytic continuation by Carlson’s theorem. This approach also shows that these identities are connected with the construction of concrete spherical functions on inductive limits of symmetric spaces. The author also observes that his identities are special cases of older formulas of R. A. Gustafson. Moreover, connections to Selberg-type integrals are discussed. Reviewer: Michael Voit (Dortmund) Cited in 5 Documents MSC: 43A85 Harmonic analysis on homogeneous spaces 33C99 Hypergeometric functions 60B05 Probability measures on topological spaces Keywords:multidimensional version of Dougall’s formula; spherical functions; series of classical symmetric space; formula of Gustafson PDFBibTeX XMLCite \textit{G. I. Ol'shanskij}, Funct. Anal. Appl. 37, No. 4, 281--301 (2003; Zbl 1075.43009); translation from Funks. Anal. Prilozh. 37, No. 4, 49--73 (2003) Full Text: DOI