Cohomology groups for recurrence relations and contiguity relations of hypergeometric systems. (Q1396416)
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scientific article; zbMATH DE number 1943312
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cohomology groups for recurrence relations and contiguity relations of hypergeometric systems. |
scientific article; zbMATH DE number 1943312 |
Statements
Cohomology groups for recurrence relations and contiguity relations of hypergeometric systems. (English)
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30 June 2003
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The theory of cohomology group for recurrence relations is developed. This research is based on the asymptotic analysis of finite difference equations carried out in the author's previous paper [Trans. Am. Math. Soc. 349, 4107--4142 (1997; Zbl 0883.39006)]. This investigation is motivated by several examples, where recurrence relations appear as contiguity relations of hypergeometric systems. The main result of the paper shows, roughly speaking, that a cochain complex (called harmonic complex) can be associated with each contiguity relation and an explicit formula describing this harmonic complex is presented.
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recurrence relation
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hypergeometric system
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contiguity relations
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Grevey extension groups
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cohomology group
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asymptotic analysis
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finite difference equations
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cochain complex
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harmonic complex
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