Journal of Mathematical Sciences

, Volume 80, Issue 5, pp 2113–2117 | Cite as

On global relations for hypergeometric series

  • V. G. Chirskii


Let [K:Q]=k, fi εK[[z]], ξ εK, Q εK[y1,...,ym]. A relation Q(f1(ξ),..., fm(ξ))=0 is called global if it holds in any local field where all fi(ξ) exist. The paper establishes that for series of the form
$$\sum\limits_{n = 0}^\infty {\frac{{(\mu _1 )_n \ldots (\mu _p )_n }}{{(\lambda _1 )_n \ldots (\lambda _{q - 1} )_n n!}}\left( {\frac{{z^{p - q} }}{{q - p}}} \right)^n , p > q,} $$
with some natural hypotheses on parameters global relations do not exist. Bibliography: 9 titles.


Local Field Hypergeometric Series Global Relation Natural Hypothesis 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. G. Chirskii

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