TABLE OF CONTENTS Regretfully, Hypergeometric Functions, Continued Fraction expansions, and elliptic integrals have received minor, if any, attention in the education of the modern engineer. They do, however, play an important role in many aspects of Astrodynamics. As examples: Gauss' classical solution to the two-body, two-point, time-constrained boundary-value problem relies heavily on a particular continued fraction expansion of the ratio of two contiguous hypergeometric functions; and, the gravitational attraction of a solid homogeneous ellipsoid upon an exterior particle is represented in terms of elliptic integrals.
Continued fraction expansions are, also, not given the prominence they deserve in the university curricula despite the fact that they are, generally, far more efficient tools for evaluating the classical functions than the more familiar infinite power series. Their convergence is typically faster and more extensive than the series and, ironically, they were in use centuries before the invention of the power series.
We shall have a number of occasions throughout this book to utilize these mathematical entities. It seems, therefore, appropriate to devote this first chapter...
