On contiguity relations of Jackson's basic hypergeometric series Υ1 (a; b; c; x, y, 1/2) and its generalizations

Osaka Journal of Mathematics

Volumn 34, Issue 1, 1997, Pages 215-221

  Date, Etsuro ^a   Horiuchi, Emi ^b  

^a OSAKA UNIVERSITY   (Japan)

^b NONE

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[No Author keywords available]

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EID: 0040563165     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. I.M. Gelfand: General theory of hypergeometric functions, Dokl. Akad. Nauk USSR 288, (1986), 14-18.
2. I.M. Gelfand and S.I. Gelfand: Generalized hypergeometric equations, ibid. 288, (1986), 279-283.
3. I.M. Gelfand, A.V. Zelevinskii and M.M. Kapranov: Hypergeometric functions and toral manifolds, Funct. Anal. and Its Appl. 23 (1989), 94-106.
4. I.M. Gelfand, V.S. Retakh and V.V. Serganova: General Airy functions, Schubert cells and Jordan grops, Dokl. Akad. Nauk USSR 298 (1988), 17-21.
5. E. Horikawa: Contiguity relations for q-hypergeometric function and related quantum group, Proc. Japan Acad. Ser. A68 (1992), 157-160.
6. E. Horikawa: Transformations and contiguity relations for Gelfand's hypergeometric functions, J. Math. Sci. Univ. Tokyo 1 (1994), 181-208.
7. F.H. Jackson: Basic double hypergeometric functions (II), The Quart. J. Math. 15 (1944), 49-61.
8. H. Kimura, Y. Haraoka and K. Takano: The generalized confluent hypergeometric functions, Proc. Japan Acad. Ser. A68 (1992), 290-295.
9. H. Kimura, Y. Haraoka and K. Takano: On confluences of the general hypergeometric systems, ibid. A69 (1993), 99-104.
10. M. Noumi: Quantum grassmannians and q-hypergeometric series, CWI Quarterly 5 (1992), 293-307.