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Hyperdeterminants. I. (English) Zbl 0866.65011
Hyperasymptotic expansions are given in terms of certain multiple integrals, the so-called hyperdeterminants. In the first section, the author gives the definition of the hyperdeterminants, and obtains several simple properties. Next section deals with an illustration of the role of the hyperdeterminants in global hyperasymptotic expansions. The main section contains a new integral representations for the hyperdeterminants. With these integral representations, the author is able to obtain convergent series expansions for the hyperdeterminants. These convergent expansions can be used to compute the hyperdeterminants to arbitrary precision.

65D20Computation of special functions, construction of tables
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI
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