Cohomology groups for recurrence relations and contiguity relations of hypergeometric systems. (English) Zbl 1035.39012

Iwasaki, Katsunori

J. Math. Soc. Japan 55, No. 2, 289-321 (2003).

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.

Reviewer: Ondřej Došlý (Brno)

MSC:

39A12	Discrete version of topics in analysis
33C10	Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

recurrence relation; hypergeometric system; contiguity relations; Grevey extension groups; cohomology group; asymptotic analysis; finite difference equations; cochain complex; harmonic complex

Citations:

Zbl 0883.39006