Expansions of generalized hypergeometric functions in series of functions of the same kind -- The t-method -- Polynomial and rational approximations to generalized hypergeometric functions -- Recursion formulas for polynomials and functions which occur in infinite series and rational approximations to generalized hypergeometric functions -- Polynomial and rational approximations for E(z)=₂F₁(1,o;p+1;-1/z) -- Polynomial and rational approximations for the incomplete gamma function -- Trapezoidal rule integration formulas -- Applications.