Geodesic
On algebraic identities between solution matrices of Bessel's and Kummer's equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 258-262 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Examples of algebraic identities between solution matrices of Bessel's and Kummer's equations and their generalizations are found. Errors in some theorems of F. Beukers and other authors are corrected.
Keywords: hypergeometric functions, Siegel's method, algebraic independence. 
@article{SEMR_2019_16_a3,
     author = {V. A. Gorelov},
     title = {On algebraic identities between solution matrices of {Bessel's} and {Kummer's} equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {258--262},
     year = {2019},
     volume = {16},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a3/}
}
TY  - JOUR
AU  - V. A. Gorelov
TI  - On algebraic identities between solution matrices of Bessel's and Kummer's equations
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 258
EP  - 262
VL  - 16
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a3/
LA  - ru
ID  - SEMR_2019_16_a3
ER  - 
%0 Journal Article
%A V. A. Gorelov
%T On algebraic identities between solution matrices of Bessel's and Kummer's equations
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 258-262
%V 16
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a3/
%G ru
%F SEMR_2019_16_a3
V. A. Gorelov. On algebraic identities between solution matrices of Bessel's and Kummer's equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 258-262. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a3/

[1] C.L. Siegel, “Über einige Anwendungen Diophantischer Approximationen”, Abh. Preuss. Acad. Wiss., Phys. – Math. Kl., 1 (1929–1930), 1–70 | Zbl

[2] Walter de Gruyter, Berlin–New York, 1989 | MR | Zbl

[3] F. Beukers, W.D. Brownawell, G. Heckman, “Siegel normality”, Annals of Math., 127 (1988), 279–308 | DOI | MR | Zbl

[4] E.R. Kolchin, “Algebraic groups and algebraic dependence”, Amer. J. Math., 90:4 (1968), 1151–1164 | DOI | MR | Zbl

[5] M.A. Cherepnev, “Algebraic independence of values of hypergeometric E-functions”, Mathematical Notes, 57:6 (1995), 630–642 | DOI | MR | Zbl

[6] IL, M., 1963 | MR | Zbl | Zbl

[7] V.A. Gorelov, “On the algebraic independence of values of generalized hypergeometric functions”, Mathematical Notes, 94:1 (2013), 82–95 | DOI | MR | Zbl

[8] V.A. Gorelov, “On algebraic identities between generalized hypergeometric functions”, Mathematical Notes, 88:4 (2010), 487–491 | DOI | MR | Zbl