On asymptotics of certain hypergeometric functions and 6-j symbols

It is known that one of the important problems of the theory of orthogonal polynomials is the problem of their asymptotic properties. The asymptotic behavior of certain orthogonal polynomials of discrete variable is studied. The polynomials are hypergeometric functions of $\sb4$F$\sb3$ type which are closely related to the transformation matrix elements--Clebsch-Gordan Coefficients and Racah Coefficients or 6-j symbols in quantum mechanics. A transformation formula and an integral representation are used to determine the asymptotic behavior of the hypergeometric functions and these coefficients. An asymptotic formula for Jacobi polynomials and Laguerre polynomials with large parameters are also derived by the use of generating functions and Darboux's method.