On hypergeometric functions in several variables II. The Wronskian of the hypergeometric functions of type (n+1, m+1)

Michitake KITA

doi:10.2969/jmsj/04540645

Michitake KITA

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 4 Pages 645-669

DOI https://doi.org/10.2969/jmsj/04540645

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Published: 1993 Received: May 18, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : On hypergeometric functions in several variables
Right : On hypergeometric functions in several variables II. The Wronskian of the hypergeometric functions of type (n+1, m+1)

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : II. The Wronskian of the hypergeometric functions of type (n+1, m+1)

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [Ao 1] K. Aomoto, On vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
[Ao 2] K. Aomoto, Les équation aux différences linéaires et les intégrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo Sect. 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. Math. Soc. Japan., 26 (1979), 519-523.
[De] P. Deligne, Equations différentielles á points singuliers réguliers, Lecture Notes in Math., 163, Springer, 1970.
[G] I.M. Gelfand, General theory of hypergeometric functions, Soviet Math. Dokl., 33 (1986), 573-577.
[G-G] I. M. Gelfand S. I. Gelfand, Generalized hypergeometric equations, Soviet Math. Dokl., 33 (1986), 643-646.
[G-Gr] I. M. Gelfand and M. I. Graev, A duality theorem for general hypergeometric functions, Soviet Math. Dokl., 34 (1987), 9-13.
[G-G-Z] I. M. Gelfand, M. I. Graev and A. V. Zelevinskii, Holonomic systems and series of hypergeometric type, Soviet Math. Dokl., 36 (1988), 5-10.
[H] A. Hattori, Topology (in Japanese), Iwanami, Tokyo, 1991.
[K-N] M. Kita and M. Noumi, On the structures of cohomology groups attached to the integral of certain many-valued analytic functions, Japan. J. of Math., 9 (1983), 113-157.
[K] M. Kita, On hypergeometric functions in several variables, (I) New integral representations of Euler type, Japan. J. of Math., 18 (1992), 25-74.
[Ko] T. Kohno, Homology of a local system on the complement of hyperplanes, Proc. Japan Acad. Ser. A, 62 (1986), 144-147.
[M] J. Mather, Notes on topological stability, mineographed notes, Harvard University, 1970.
[M-S-T-Y] K. Matsumoto, T. Sasaki, N. Takayama and M. Yoshida, Monodromy of the hypergeometric differential equation of type (k,n) I, 1992, preprint.
[M-S-Y] K. Matsumoto, T. Sasaki and M. Yoshida, The monodromy of the period map of a 4-parameter family of K3 surfaces and the hypergeometric function of type (3, 6), International J. of Math., 3 (1992), 1-164.
[S] T. Sasaki, Contiguity relations of Aomoto-Gelfand hypergeometric functions and applications to Appell's system F₃ and Goursat's system ₃F₂, SIAM J. Math. Anal., 22 (1991), 821-846.
[V1] A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I., Math. USSR-Izv., 35 (1990), 543-571.
[V2] A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. II., Math. USSR-Izv., 36 (1991), 155-167. ?Hypergeometric functions in several variables 669

Right : [Ao 1] K. Aomoto, On vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
[Ao 2] K. Aomoto, Les équation aux différences linéaires et les intégrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo Sect. IA, 22 (1975), 271-297 and: Une correction et un complément à l'article “Les équations aux différences linéaires et les intégrales des fonctions multiformes”. J. Fac. Sci. Univ. Tokyo Sect. IA, 26 (1979), 519-523.
[De] P. Deligne, Equations différentielles á points singuliers réguliers, Lecture Notes in Math., 163, Springer, 1970.
[G] I. M. Gelfand, General theory of hypergeometric functions, Soviet Math. Dokl., 33 (1986), 573-577.
[G-G] I. M. Gelfand S. I. Gelfand, Generalized hypergeometric equations, Soviet Math. Dokl., 33 (1986), 643-646.
[G-Gr] I. M. Gelfand and M. I. Graev, A duality theorem for general hypergeometric functions, Soviet Math. Dokl., 34 (1987), 9-13.
[G-G-Z] I. M. Gelfand, M. I. Graev and A. V. Zelevinskii, Holonomic systems and series of hypergeometric type, Soviet Math. Dokl., 36 (1988), 5-10.
[H] A. Hattori, Topology (in Japanese), Iwanami, Tokyo, 1991.
[K-N] M. Kita and M. Noumi, On the structures of cohomology groups attached to the integral of certain many-valued analytic functions, Japan. J. of Math., 9 (1983), 113-157.
[K] M. Kita, On hypergeometric functions in several variables, (I) New integral representations of Euler type, Japan. J. of Math., 18 (1992), 25-74.
[Ko] T. Kohno, Homology of a local system on the complement of hyperplanes, Proc. Japan Acad. Ser. A, 62 (1986), 144-147.
[M] J. Mather, Notes on topological stability, mineographed notes, Harvard University, 1970.
[M-S-T-Y] K. Matsumoto, T. Sasaki, N. Takayama and M. Yoshida, Monodromy of the hypergeometric differential equation of type (k,n) I, 1992, preprint.
[M-S-Y] K. Matsumoto, T. Sasaki and M. Yoshida, The monodromy of the period map of a 4-parameter family of K3 surfaces and the hypergeometric function of type (3,6), International J. of Math., 3 (1992), 1-164.
[S] T. Sasaki, Contiguity relations of Aomoto-Gelfand hypergeometric functions and applications to Appell's system F₃ and Goursat's system ₃F₂, SIAM J. Math. Anal., 22 (1991), 821-846.
[V1] A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I., Math. USSR-Izv., 35 (1990), 543-571.
[V2] A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. II., Math. USSR-Izv., 36 (1991), 155-167.

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