Abstract
Abstract The starting point and the major object of study of this book is the ordinary linear homogeneous second-order differential equation with polynomial coefficients P0(z), P1 (z), P2(z) considered in the complex z plane. The primes in (1.1.1) indicate differentiation with respect to z. It is supposed that the polynomials in (1.1.1) do not possess common factors depending on z. The degrees of the polynomials P0, P1, P2 are denoted by k0, k1, k2. Beyond the z plane as the range of definition for eqn (1.1.1), the Riemann sphere can be considered. This al1ows us to incJude the point z = ∞ in our studies. The complex z plane including the point z ∞ is denoted by ℂ. Equation (1 .1.1) has two linearly independent solutions. The general solution of eqn (1.1.1) is an arbitrary linear combination of these particular solutions.
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