A series solution for certain Riccati equations with applications to Sturm-Liouville problems (Q1119796)

Series solutions for the two related equations \(\lambda -q(t)+r'(t)+r^ 2(t)=0\) and \(y''+(\lambda -q(t))y(t)=0\) for \(t\in (a,b)\), \(b\leq \infty\), \(\lambda\) real and positive, \(q\in L(a,b)\) are obtained. Two main theorems and four corollaries are proved correspondingly.