journal article Jan 01, 1992

On Hypergeometric Functions in Several Variables 1. New integral representations of Euler type

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References
31
[1]
[Ao1] K. Aomoto, On vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255. 10.2969/jmsj/02720248
[2]
[Ao2] K. Aomoto, Les equation aux différences linéaires et les integrales des fonctions multi formes, J. Fac. Sci. Univ. Tokyo. Sec. IA, 22 (1975), 271-297 and: Une correction et un complément à Particle “Les équations aux différences linéaires et les intégrales des fonctions multiformes”, J. Fac. Sci. Univ. Tokyo. Sec. IA, 26 (1979), 519-523.
[3]
[Ao3] K. Aomoto, Configurations and invariant theory of Gauss-Manin systems, in Group Rep resentations and System of Differential Equations, Advanced Studies in Pure Mathe matics, 4, 1984, Kinokuniya.
[4]
[Ao4] K. Aomoto, Finiteness of a cohomology associated with certain Jackson integrals, sub mitted to Tohoku J. of Math.
[5]
[Ao5] K. Aomoto, q-analogue of de Rham cohomology associated with Jackson integrals (I), (II), submitted to Proc. J. Acad.
[6]
[A-K] P. Appell et J. Kampé de Feriet, Fonctions hypergéométriques et hypersphériques, poly nomes d'Hermite, Gauthier-Villars, Paris, 1926.
[7]
[Be] G. Belardinelli, Fonctions hypergéométriques de plusieurs variables et résolutions analy tiques des équations algèbriques générales, Gauthiers-Villars, Paris, 1960.
[8]
[Bi] R. Birkeland, Une proposition générale sur les fonctions hypergéométriques de plusieurs variables, C. R. Acad. Sci., 185 (1927), 923-925.
[9]
[De] P. Deligne, Équations différentielles à points singuliers réguliers Lecture Notes in Math. 163, Berlin-Heiderberg-New York: Springer-Verlag, 1970.
[10]
[Di] P. G. L. Dirichlet, Sur une nouvelle méthode pour la détermination des intégrales multi ples, Werke, Bd. I., 375-380, Chelsea, New York, 1969. 10.1017/cbo9781139237338.027
[11]
[Er1] A. Erdélyi, Higher transcendental functions, vol. I, Mac Graw-Hill, 1953.
[12]
[Er2] A. Erdélyi, Hypergeometric functions of two variables, Acta Math., 83 (1950), 131-164. 10.1007/bf02392635
[13]
[G] LM. Gelfand, General theory of hypergeometric functions, Soviet Math. Dokl., 33 (1986), 573-577.
[14]
[G-G] LM. Gelfand and S. I. Gelfand, Generalized hypergeometric equations, Soviet Math. Dokl., 33 (1986), 643-646.
[15]
[G-Gr] LM. Gelfand and MI. Graev, A duality theorem for general hypergeometric functions, Soviet Math. Dokl., 34 (1987) 9-13.
[16]
[G-G-Z] LM. Gelfand, MI. Graev and A.V. Zelevinskii, Holonomic systems and series of hyper geometric type, Soviet Math. Dokl., 36 (1988) 5-10.
[17]
[Ha] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, reprinted by Dover, New York; 1952.
[18]
[Ho1] J. Horn, Über die Konvergenz der hypergeometrischen Reihen zweier and dreier Veranderlichen, Math. Ann., 34 (1889), 544-600. 10.1007/bf01443681
[19]
[Ho2] J. Horn, Hypergeometriche Funktionen zweier Veranderlichen, Math. Ann., 105 (1931), 381-407. 10.1007/bf01455825
[20]
[Ka] J. Kaneko, Monodromy group of Appell's system (F4), Tokyo J. Math., 4 (1981), 35-54. 10.3836/tjm/1270215739
[21]
[Ki] M. Kita, On the Aomoto-Gelfand hypergeometric functions and twisted de Rham coho mology, preprint, 1990.
[22]
[K-N] M. Kita and M. Noumi, On the structure of cohomology groups attached to the integral of certain many-valued analytic functions, Japan. J. Math., 9 (1983), 113-157. 10.4099/math1924.9.113
[23]
[Ku] E. Kummer, De integralibus definitis et seriebus infinitis, J. Reine Angew. Math., 17 (1837), 210-227.
[24]
[M] Hj. Mellin, Über den Zusammenhang zwischen den linearen Differential and Differen zengleichung, Acta Math., 25 (1902), 139-164. 10.1007/bf02419024
[25]
[O] O. Ore, Sur la forme des fonctions hypergéométriques de plusieurs variables, J. Math. purer et appl., 9 (1930), 311-326.
[26]
[P] PT. Pastro, On the integral representation of F<sub>4</sub> of Appell and its Lauricella generaliza tion, Bull. Sci. Math., 113 (1989), 119-124.
[27]
[S-S-M] M. Sato, Sato's theory of prehomogeneous vector spaces, algebraic part. An English translation from Shintani's note, translated by M. Muro, Nagoya J. Math., 120 (1990), 1-34. 10.1017/s0027763000003214
[28]
[T-K] A. Tsuchiya and Y. Kanie, Fock space representations of the Virasoro algebra Inter twining operators, Publ. Res. Inst. Math. Sci., 22 (1986), 259-327. 10.2977/prims/1195178069
[29]
[W-W] E. T. Whittaker and G.N. Watson, A course of modern analysis, Cambridge Univ. Press, 1963.
[30]
[Yo1] M. Yoshida, Euler integral transformations of hypergeometric functions of two variables, Hiroshima Math. J., 10 (1980), 329-335. 10.32917/hmj/1206134456
[31]
[Yo2] M. Yoshida, Fuchsian differential equations, Vieweg-Verlag, Wiesbaden, 1987. 10.1007/978-3-663-14115-0
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Details
Published
Jan 01, 1992
Vol/Issue
18(1)
Pages
25-74
Cite This Article
Michitake KITA (1992). On Hypergeometric Functions in Several Variables 1. New integral representations of Euler type. Japanese journal of mathematics. New series, 18(1), 25-74. https://doi.org/10.4099/math1924.18.25