Geodesic
On the Algebraic Independence of Values of Generalized Hypergeometric Functions
Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 94-108

Voir la notice de l'article provenant de la source Math-Net.Ru

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, differential field, transcendence degree, contiguous functions.
Mots-clés : Galois group 
@article{MZM_2013_94_1_a7,
     author = {V. A. Gorelov},
     title = {On the {Algebraic} {Independence} of {Values} of {Generalized} {Hypergeometric} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {94--108},
     publisher = {mathdoc},
     volume = {94},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a7/}
}
TY  - JOUR
AU  - V. A. Gorelov
TI  - On the Algebraic Independence of Values of Generalized Hypergeometric Functions
JO  - Matematičeskie zametki
PY  - 2013
SP  - 94
EP  - 108
VL  - 94
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a7/
LA  - ru
ID  - MZM_2013_94_1_a7
ER  - 
%0 Journal Article
%A V. A. Gorelov
%T On the Algebraic Independence of Values of Generalized Hypergeometric Functions
%J Matematičeskie zametki
%D 2013
%P 94-108
%V 94
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a7/
%G ru
%F MZM_2013_94_1_a7
V. A. Gorelov. On the Algebraic Independence of Values of Generalized Hypergeometric Functions. Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 94-108. http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a7/