Reducibility and linear reducibility of linear differential equations (Q752276)

The author considers the homogeneous linear differential equation of order \(n+m\) (`hypergeometric equation') \[ (1)\quad \{\prod^{n+m}_{j=1}(\delta +n\lambda_ j)-z^ n\prod^{m}_{j=1}(\delta +n\nu_ j)\}(y)=0 \] where \(\delta =z(d/dz)\), \(z\in {\mathbb{C}}\). The problem of linear reducibility of equation (1) was investigated in the author's paper [Russ. Math. Surv. 41, No.3, 231-232 (1986); translation from Usp. Mat. Nauk 41, No.3(249), 201-202 (1986; Zbl 0611.10022)]. Here he presents examples of equations (1) which are reducible or linear reducible on the field of algebraic functions.