Geodesic
General Linear Transformations of Hypergeometric Functions
Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 769-779

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

The notion of a canonical form is introduced for multiple hypergeometric series. This notion, in conjunction with the factorization method suggested earlier by the author, is used to obtain the most general explicit descriptions of linear transformations of multiple series that are of Gauss, Kummer, or Bessel type with respect to some variable $x_n$. A complete classification of the 34 Horn series according to their types and forms is given. It is used to show that the transformations described in this paper permit one to obtain the 147 single transformations of Horn series as well as quite a few repeated transformations. A computer program implementing these transformations is developed on the basis of the Maple V-4 computer algebra system. 
@article{MZM_2001_70_5_a11,
     author = {A. W. Niukkanen},
     title = {General {Linear} {Transformations} of {Hypergeometric} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {769--779},
     publisher = {mathdoc},
     volume = {70},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a11/}
}
TY  - JOUR
AU  - A. W. Niukkanen
TI  - General Linear Transformations of Hypergeometric Functions
JO  - Matematičeskie zametki
PY  - 2001
SP  - 769
EP  - 779
VL  - 70
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a11/
LA  - ru
ID  - MZM_2001_70_5_a11
ER  - 
%0 Journal Article
%A A. W. Niukkanen
%T General Linear Transformations of Hypergeometric Functions
%J Matematičeskie zametki
%D 2001
%P 769-779
%V 70
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a11/
%G ru
%F MZM_2001_70_5_a11
A. W. Niukkanen. General Linear Transformations of Hypergeometric Functions. Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 769-779. http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a11/