Keywords: hypergeometric equations, generating functions.
@article{TMF_2004_140_1_a0,
author = {A. M. Perelomov},
title = {Hypergeometric {Solutions} of {Some} {Algebraic} {Equations}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {3--13},
year = {2004},
volume = {140},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_1_a0/}
}
A. M. Perelomov. Hypergeometric Solutions of Some Algebraic Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 1, pp. 3-13. http://geodesic.mathdoc.fr/item/TMF_2004_140_1_a0/
[1] M. A. Olshanetsky, A. M. Perelomov, Phys. Rep., 94:6 (1983), 313–404 | DOI | MR
[2] N. H. Abel, J. Reine Angew. Math., 1 (1826), 65–84 | DOI | MR | Zbl
[3] Ch. Hermite, Compt. Rend., 46 (1858), 508–515
[4] L. Kronecker, Compt. Rend., 46 (1858), 1150–1152
[5] F. Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichung $5^{ten}$ Grades, Teubner, Leipzig, 1884 | MR
[6] J. Cockle, Phil. Mag., 20 (1860), 145–148
[7] H. Umemura, “Solution of algebraic equations by theta constants”, Appendix to Tata Lectures on Theta, V. II, ed. D. Mumford, Birkhauser, Boston, MA, 1984, 3.261–3.272 | MR
[8] H. Schwarz, J. Reine Angew. Math., 75 (1873), 292–335 | DOI | MR
[9] F. Beukers, G. Heckman, Invent. Math., 95 (1989), 325–354 | DOI | MR | Zbl
[10] R. Fricke, Lehrbuch der Algebra, Vieweg und Sohn, Braunschweig, 1924 | Zbl
[11] M. L. Glasser, J. Comput. Appl. Math., 118 (2000), 169–173 | DOI | MR | Zbl
[12] L. Pochhammer, J. Reine Angew. Math., 102 (1888), 76–159 | MR
[13] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, T. 1, Nauka, M., 1973 | MR
[14] B. Riemann, Abh. König. Gesell. Wiss. zu Göttingen, 7 (1857), 1–24