Abstract
This chapter focuses on continued fractions applicable to linear second-order ordinary differential equations. A solution in terms of a continued fraction is obtained. By finding a simple recurrence pattern, the logarithmic derivative of the solution to an ordinary differential equation in terms of a continued fraction is expressed. The continued fraction can be extended indefinitely. The partial sums for the continued fraction can also be evaluated. This technique has rarely been extended, with any generality, to any types of differential equations other than linear second-order ordinary differential equations. By taking partial sums of the continued fraction in, successively better approximations may be found.
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