ABSTRACT

The importance of equation (8.01) stems in part from the following theorem, the proof of which is the theme of this section.' Theorem 8.1 Any homogeneous linear differential equation of the second order whose singularities-including the point at infinity-are regular and not more than three in number, is transformable into the hypergeometric equation. 8.2 We first construct the second-order equation

having regular singularities at given distinct finite points t , q, and C, with arbitrarily assigned exponent pairs (a,, a,), (PI, P,), and (y , , y,), respectively.'