Se p 20 03 BIVARIATE HYPERGEOMETRIC D - MODULES
نویسندگان
چکیده
We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are regular holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank.
منابع مشابه
m at h . A G ] 2 3 A ug 2 00 4 BIVARIATE HYPERGEOMETRIC D - MODULES
We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank.
متن کاملDefinite Sums of Hypergeometric Terms and Limits of P-Recursive Sequences
The ubiquity of the class of D-finite functions and P-recursive sequences in symbolic computation is widely recognized. This class is defined in terms of linear differential and difference equations with polynomial coefficients. In this thesis, the presented work consists of two parts related to this class. In the first part, we generalize the reduction-based creative telescoping algorithms to ...
متن کاملar X iv : a st ro - p h / 03 09 41 9 v 1 1 6 Se p 20 03 Discovery of the Bright Afterglow of the Nearby Gamma - Ray Burst of 29 March 2003
X iv :a st ro -p h/ 03 09 41 9v 1 1 6 Se p 20 03 Discovery of the Bright Afterglow of the Nearby Gamma-Ray Burst of 29 March 2003 P. A. Price, D. W. Fox, S. R. Kulkarni, B. A. Peterson, B. P. Schmidt, A. M. Soderberg, S. A. Yost, E. Berger, S. G. Djorgovski, D. A. Frail, F. A. Harrison, R. Sari, A. W. Blain, and S. C. Chapman. 1 RSAA, ANU, Mt. Stromlo Observatory, via Cotter Rd, Weston Creek, A...
متن کاملApplicability of the q-analogue of Zeilberger's algorithm
The applicability or terminating condition for the ordinary case of Zeilberger’s algorithm was recently obtained by Abramov. For the qanalogue, the question of whether a bivariate q-hypergeometric term has a qZ-pair remains open. Le has found a solution to this problem when the given bivariate q-hypergeometric term is a rational function in certain powers of q. We solve the problem for the gene...
متن کاملUniform convergence of hypergeometric series
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.
متن کامل