Linear Differential Equations in a Sector of the Complex Plane

Abstract

In this chapter we consider a single linear differential equation of nth order of the form

$$ F(x,z) \equiv {x^{(n)}} + {a_1}(z){x^{(n - 1)}} + ... + {a_n}(z)x = 0 $$

(12.1)

in a central sector S of the complex plane for sufficiently large argument z where a ₁(z),..., a _n (z) are holomorphic functions.