A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions

[1]

G E. Andrews, R. Askey, and R. Roy. Special functions, volume 71 of Encyclopedia of

Mathematics and its Applications. Cambridge University Press, Cambridge, 1999.

[2]

VI.S. Dotsenko, V.A. Fateev: Conformal algebra and multipoint correlation functions in 2D

statistical models, Nucl. Phys. B240[FS12] (1984), 312–348.

[3]

A. Ebisu: Invariants of difference equations and transformation formulae for hypergeometric

functions, in preparation.

[4]

A. Ebisu and H. Ochiai: Difference equations for 4 F3 (1), in preparation.

[5]

Y. Haraoka: Prolongability of ordinary differential equations, J. non-lin. Math. Physics, 20,

Supplement 1 (2013), 70–84.

[6]

Y. Haraoka: On Oshima’s middle convolution, Josai Math. Monographs 12 (2020), 19–51.

[7]

E. J. Wilczynski, Projective Differential Geometry of Curves and Ruled Surfaces, reprinted

by Chelsea Pub. Co., Teubner, 1906.

[8]

J. A. Wilson, Three-term contiguous relations and some new orthogonal polynomials. In

Pad´e and rational approximation (Proc. Internat. Sympos., Univ. South Florida, Tampa,

Fla., 1976), 227 – 232, Academic Press, New York, 1977.

Akihito Ebisu

Faculty of Information and Computer Science, Chiba Institute of Technology,

Chiba 275-0023, Japan

email: akihito.ebisu@p.chibakoudai.jp

Yoshishige Haraoka

Department of Mathematics, Kumamoto University,

Kumamoto 860-8555, Japan

email: haraoka@kumamoto-u.ac.jp

Masanobu Kaneko

Department of Mathematics, Kyushu University,

Fukuoka 819-0395, Japan

email: mkaneko@math.kyushu-u.ac.jp

Hiroyuki Ochiai

Department of Mathematics, Kyushu University,

Fukuoka 819-0395, Japan

email: ochiai@imi.kyushu-u.ac.jp

Takeshi Sasaki

Kobe University,

Kobe 657-8501, Japan

email: sasaki@math.kobe-u.ac.jp

Masaaki Yoshida

Kyushu University,

Fukuoka 819-0395, Japan

email: myoshida@math.kyushu-u.ac.jp

...