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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 94–108
DOI: https://doi.org/10.4213/mzm9256 (Mi mzm9256) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the Algebraic Independence of Values of Generalized Hypergeometric Functions

V. A. Gorelov

Moscow Power Engineering Institute (Technical University)
Full-text PDF (552 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm9256
Abstract: We consider hypergeometric functions satisfying homogeneous linear differential equations of arbitrary order. We prove general theorems on the algebraic independence of the solutions of a set of hypergeometric equations as well as of the values of these solutions at algebraic points. The conditions of most theorems are necessary and sufficient.
Keywords: generalized hypergeometric function, linear differential equation, algebraic independence of solutions, Galois group, differential field, transcendence degree, contiguous functions.
Received: 29.09.2011
Revised: 17.05.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 82–95
DOI: https://doi.org/10.1134/S0001434613070080
Bibliographic databases:
Document Type: Article
UDC: 511.36
Language: Russian
Citation: V. A. Gorelov, “On the Algebraic Independence of Values of Generalized Hypergeometric Functions”, Mat. Zametki, 94:1 (2013), 94–108; Math. Notes, 94:1 (2013), 82–95
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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