Geodesic
Hypergeometric functions over an arbitrary field
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 5, pp. 831-905 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper is devoted to the definition and investigation of hypergeometric functions over an arbitrary continuous locally compact field or a finite field, based on the author's earlier definition of generalized hypergeometric function over the field $\mathbb R$. 
@article{RM_2004_59_5_a1,
     author = {I. M. Gel'fand and M. I. Graev and V. S. Retakh},
     title = {Hypergeometric functions over an arbitrary field},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {831--905},
     year = {2004},
     volume = {59},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2004_59_5_a1/}
}
TY  - JOUR
AU  - I. M. Gel'fand
AU  - M. I. Graev
AU  - V. S. Retakh
TI  - Hypergeometric functions over an arbitrary field
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 831
EP  - 905
VL  - 59
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/RM_2004_59_5_a1/
LA  - en
ID  - RM_2004_59_5_a1
ER  - 
%0 Journal Article
%A I. M. Gel'fand
%A M. I. Graev
%A V. S. Retakh
%T Hypergeometric functions over an arbitrary field
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 831-905
%V 59
%N 5
%U http://geodesic.mathdoc.fr/item/RM_2004_59_5_a1/
%G en
%F RM_2004_59_5_a1
I. M. Gel'fand; M. I. Graev; V. S. Retakh. Hypergeometric functions over an arbitrary field. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 5, pp. 831-905. http://geodesic.mathdoc.fr/item/RM_2004_59_5_a1/

[1] K. Aomoto, K. Iguchi, “On quasi-hypergeometric functions”, Methods Appl. Anal., 6:1 (1999), 55–66 | MR | Zbl

[2] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, 1, Nauka, M., 1973

[3] I. M. Gelfand, “Obschaya teoriya gipergeometricheskikh funktsii”, Dokl. AN SSSR, 288:1 (1986), 14–18 | MR | Zbl

[4] I. M. Gelfand, M. I. Graev, “$GG$-funktsii mnogikh peremennykh i ikh svyaz s obschimi gipergeometricheskimi funktsiyami”, UMN., 52:4 (1997), 3–48 | MR | Zbl

[5] I. M. Gelfand, M. I. Graev, “Gipergeometricheskie funktsii nad konechnymi polyami”, Dokl. RAN, 381:6 (2001), 732–737 | MR | Zbl

[6] I. M. Gelfand, M. I. Graev, “$\mathscr N$-funktsii i ikh svyaz s resheniyami obschikh gipergeometricheskikh sistem i $GG$-sistem”, UMN., 56:4 (2001), 3–34 | MR | Zbl

[7] I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro, Teoriya predstavlenii i avtomorfnye funktsii, Nauka, M., 1966 | MR

[8] I. M. Gelfand, M. I. Graev, V. S. Retakh, “Obschie gipergeometricheskie sistemy uravnenii i ryady gipergeometricheskogo tipa”, UMN, 47:4 (1992), 3–82 | MR | Zbl

[9] I. M. Gelfand, M. I. Graev, A. V. Zelevinskii, “Golonomnye sistemy uravnenii i ryady gipergeometricheskogo tipa”, Dokl. AN SSSR, 295:1 (1987), 14–19 | MR | Zbl

[10] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, M., 1958 | Zbl

[11] I. M. Gelfand, A. V. Zelevinskii, M. M. Kapranov, “Gipergeometricheskie funktsii i toricheskie mnogoobraziya”, Funkts. analiz i ego pril., 23:2 (1989), 12–26 | MR | Zbl

[12] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1962

[13] R. Lidl, G. Niderraiter, Konechnye polya, t. 1, Nauka, M., 1988