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The efficient evaluation of the hypergeometric function of a matrix argument. (English) Zbl 1117.33007
This paper focuses on the expansion of matrix argument generalized hypergeometric functions ( p F q ) as a series of Jack functions. The main purpose in fact is the approximation of these type functions by truncating these series. The authors first mention the previous approaches to this end. Then they propose their own technique. They conjecture and show that the computational complexity of their method is linear in the size of the matrix appearing as the argument of the concerned generalized hypergeometric function. Their work contains also certain theorems about the validation of the efficiency of their method.
MSC:
33C20Generalized hypergeometric series, p F q
65B10Summation of series (numerical analysis)
05A99Classical combinatorial problems