On Algebraic Identities between Generalized Hypergeometric Functions
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 511-516 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we obtain new algebraic identities between hypergeometric functions satisfying linear differential equations of arbitrary order as well as between the fundamental matrices of hypergeometric equations.
Keywords: hypergeometric function, algebraic identity, linear differential equation, hypergeometric equation, fundamental matrix, Kummer's identity, Euler's identity.
@article{MZM_2010_88_4_a2,
     author = {V. A. Gorelov},
     title = {On {Algebraic} {Identities} between {Generalized} {Hypergeometric} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {511--516},
     year = {2010},
     volume = {88},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a2/}
}
TY  - JOUR
AU  - V. A. Gorelov
TI  - On Algebraic Identities between Generalized Hypergeometric Functions
JO  - Matematičeskie zametki
PY  - 2010
SP  - 511
EP  - 516
VL  - 88
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a2/
LA  - ru
ID  - MZM_2010_88_4_a2
ER  - 
%0 Journal Article
%A V. A. Gorelov
%T On Algebraic Identities between Generalized Hypergeometric Functions
%J Matematičeskie zametki
%D 2010
%P 511-516
%V 88
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a2/
%G ru
%F MZM_2010_88_4_a2
V. A. Gorelov. On Algebraic Identities between Generalized Hypergeometric Functions. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 511-516. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a2/

[1] Yu. Lyuk, Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980 | MR | Zbl

[2] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1965 | MR | Zbl

[3] C. L. Siegel, “Über einige Anwendungen diophantischer Approximationen”, Abhandlungen Akad. Berlin, 1929, no. 1, 70 pp. | Zbl

[4] C. L. Siegel, Transcendental Numbers, Ann. of Math. Stud., 16, Princeton Univ. Press, Princeton, NJ, 1949 | MR | Zbl

[5] A. B. Shidlovskii, Transtsendentnye chisla, Nauka, M., 1987 | MR | Zbl

[6] Yu. V. Nesterenko, “Priblizheniya Ermita–Pade obobschennykh gipergeometricheskikh funktsii”, Matem. sb., 185:10 (1994), 39–72 | MR | Zbl

[7] V. Kh. Salikhov, G. G. Viskina, “Algebraicheskie sootnosheniya mezhdu gipergeometricheskoi $E$-funktsiei i ee proizvodnymi”, Matem. zametki, 71:6 (2002), 832–844 | MR | Zbl

[8] E. L. Ains, Obyknovennye differentsialnye uravneniya, Kharkov, 1939 | Zbl

[9] Dzh. Sansone, Obyknovennye differentsialnye uravneniya, v. 1, IL, M., 1953 | MR | Zbl

[10] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971 | MR | Zbl