Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities.
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.
multidimensional version of Dougall's formula
scientific article; zbMATH DE number 2138546