On rational De Rham cohomology associated with the generalized airy function

Hironobu Kimura

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 2, page 351-366
  • ISSN: 0391-173X

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Kimura, Hironobu. "On rational De Rham cohomology associated with the generalized airy function." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.2 (1997): 351-366. <http://eudml.org/doc/84262>.

@article{Kimura1997,
author = {Kimura, Hironobu},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Airy function; generalized Airy function; de Rham complex},
language = {eng},
number = {2},
pages = {351-366},
publisher = {Scuola normale superiore},
title = {On rational De Rham cohomology associated with the generalized airy function},
url = {http://eudml.org/doc/84262},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Kimura, Hironobu
TI - On rational De Rham cohomology associated with the generalized airy function
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 2
SP - 351
EP - 366
LA - eng
KW - Airy function; generalized Airy function; de Rham complex
UR - http://eudml.org/doc/84262
ER -

References

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  2. [AGV] V. Arnold - A. Varchenko - S. Goussein-Zadé, Singularité des applications différentiables, Vol. 1-2, Mir, Moscow, 1986. 
  3. [G] Godement, Topologie algébrique et théorie des faisceaux, Herman, Paris, 1958. Zbl0080.16201
  4. [GRS] I.M. Gelfand - V.S. Retahk, V.V. Serganova, GeneralizedAiryfunctions, Schubert cells, and Jordan groups, Dokl. Akad. Nauk. SSSR298 (1988), 17-21; English transl. in Soviet Math. Dokl. 37 (1988), 8-12. Zbl0699.33012
  5. [HK] Y. Haraoka - H. Kimura, Contiguity relations of the generalized confluent hypergeometric functions, Proc. Japan Acad. 69 (1993), 105-110. Zbl0812.33007
  6. [IKSY] K. Iwasaki - H. Kimura - S. Shimomura - M. Yoshida, From Gauss to Painlevé, Vieweg, Wiesbaden, 1991. Zbl0743.34014
  7. [K1] H. Kimura, The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure, Ann. Mat. Pura App. 155 (1989), 25-74. Zbl0693.34043
  8. [K2] H. Kimura, On rational de Rham cohomology associated with the generalized confluent hypergeometric functions I, P1 case, to appear in Royal Society of Edimburgh. Zbl0883.33009
  9. [K3] H. Kimura, On Wronskian determinants of the generalized confluent hypergeometric functions, (1994). preprint. 
  10. [KHT1] H. Kimura - Y. Haraoka - K. Takano, The generalized confluent hypergeometric functions, Proc. Japan Acad. 68 (1992), 290-295. Zbl0773.33004
  11. [KHT2] H. Kimura - Y. Haraoka - K. Takano, On confluences of the general hypergeometric systems, Proc. Japan Acad. 69 (1993), 99-104. Zbl0822.33007
  12. [KHT3] H. Kimura - Y. Haraoka - K. Takano, On contiguity relations of the confluent hypergeometric systems, Proc. Japan Acad. 70 (1994), 47-49. Zbl0798.33009
  13. [KK] H. Kimura - T. Koitabashi, Normalizer of maximal abelian subgroups of GL(n) confluent hypergeometric functions, Kumamoto J. Math.9 (1996), 13-43. Zbl0848.33009
  14. [Mac] I.G. Macdonald, Symmetric functions and Hall polynomials, Oxford University Press, Oxford, 1979. Zbl0487.20007
  15. [M] H. Matsumura, Commutative algebra, second edition, Benjamin, 1980. Zbl0441.13001
  16. [N] M. Noumi, Expansion of the solutions of a Gauss-Manin system at a point of infinity, Tokyo J. Math.7 (1984), 1-60. Zbl0554.32009
  17. [O] K. Okamoto, Isomonodromic deformation and Painlevé equations and the Garnier system, J. Fac. Sci. Univ. Tokyo Sec. IA, Math.33 (1986), 576-618. Zbl0631.34011
  18. [OK] K. Okamoto - H. Kimura, On particular solutions of Garnier systems and the hypergeometric functions of several variables, Quarterly J. Math.37 (1986), 61-80. Zbl0597.35114

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