On applications of hypergeometric functions

摘要

This is a survey article on the author's involvement over the years with hypergeometric functions. We discuss our counter-example to one of M. Robertson's conjectures, our results on the omitted values problems, Brannan's conjecture on the coefficients of a certain power series, generalizations of Ramanujan's asymptotic formulas for complete elliptic integrals and Muir's 1883 approximation to the arc length of an ellipse involving an inequality for some 3F2's.