Abstract
A simple necessary and sufficient condition is given for the solutions of Q = 0 Q = 0 to be free of movable branch points. And, when the condition is satisfied, all the solutions of Q = 0 Q = 0 can be obtained by solving linear differential equations of order ≤ 2 \leq 2 . There are four mutually exclusive cases. We shall relate Case 4 to less convenient conditions P. Appell had introduced. We shall also show how Cases 3 and 4 together motivated our discovery of an identity that is essential for a satisfactory theory of relative invariants for homogeneous linear differential equations.
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