Abstract
The authors had presented the general foundations for a theory of hypergeometric functions of matrix argument over real division algebras. Here, they further develop the fine structure of these functions over the complex field, including series expansions, integral representations, asymptotics, differential equations, addition formulas, multiplication formulas, summation theorems, transformation properties, etc. Especially important are the operator-valued hypergeometric functions, required for (nonspherical) expansions such as addition formulas by the noncommutativity of matrix multiplication
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