Hiroshima Mathematical Journal

On the structure of connection coefficients for hypergeometric systems

Toshiaki Yokoyama

Full-text: Open access

Article information

Hiroshima Math. J., Volume 18, Number 2 (1988), 309-339.

First available in Project Euclid: 21 March 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39A10: Difference equations, additive
Secondary: 34A08: Fractional differential equations


Yokoyama, Toshiaki. On the structure of connection coefficients for hypergeometric systems. Hiroshima Math. J. 18 (1988), no. 2, 309--339. doi:10.32917/hmj/1206129726. https://projecteuclid.org/euclid.hmj/1206129726

Export citation


  • [1] W. Balser, W. B. Jurkat and D. A. Lutz, On the reduction of connection problems for differential equations with an irregular singular point to ones with only regular singularities, I., SIAM J. Math. Anal., 12 (1981), 691-721.
  • [2] G. D. Birkhoff, General theory of linear difference equations, Trans. Amer. Math. Soc., 12 (1911), 243-284.
  • [3] B. L. J. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes-integrals, Compositio Math., 15 (1964), 239-341.
  • [4] H. Galbrun, Sur la representation des solutions d'une equation lineaire aux differences finies pour les grandes valeurs de la variable, Acta Math., 36 (1913), 1-68.
  • [5] M. Kohno, A connection problem for hypergeometric systems, Funkcial. Ekvac., to appear.
  • [6] M. Kohno, Frobenius' theorem and Gauss-Kummer's formula, Funkcial. Ekvac., 28 (1985), 249-266.
  • [7] M. Kohno and T. Suzuki, Reduction of single Fuchsian differential equations to hypergeometric systems, Kumamoto J. Sci. (Math.), 17 (1987), 27-74.
  • [8] N. E. Norlund, Hypergeometric functions, Acta Math., 94 (1955), 289-349.
  • [9] K. Okubo, Connection problems for systems of linear differential equations, in Lecture Notes in Math. 243, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
  • [10] K. Okubo, On the group of Fuchsian equations, Progress Report for Grant-in-Aid for Scientific Research, 1981.
  • [11] F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York and London, 1974.
  • [12] R. Schafke, Uber das globale analytische Verhalten der Losungen der ber die Laplacetransformation zusammenhangenden Differentialgleichungen tx'=(A + fB)x und (s--B)f=(p -- A)v, Dissertation, Univ. Essen, 1979.
  • [13] T. Yokoyama, On connection formulas for a fourth order hypergeometric system, Hiroshima Math. J., 15 (1985), 297-320.
  • [14] T. Yokoyama, Characterization of connection coefficients for hypergeometric systems, Hiroshima Math. J., 17 (1987), 225-239.