Approximation of the Jacobi polynomials and the Racah coefficients (Q983497)

This paper is a continuation of the studies of the authors in [Rocky Mt. J. Math. 37, No.1, 159--184 (2007; Zbl 1193.33024)] which provides extensions of the earlier obtained results to a subinterval of the interval of orthogonality \((-1,1)\) of the Jacobi polynomials \(P_{n}^{(\alpha, \beta)}(x)\). More specifically, the authors obtain asymptotic approximations to the Jacobi polynomials \(P_{n}^{(\alpha, \beta)}(x)\) and to the Racah coefficients \(P_{n}^{(an+c, bn+d)}(x)\), as \(n\rightarrow \infty\), where \(a,b,c,d\) are constants. The approximations to \(P_{n}^{(\alpha, \beta)}(x)\) are generated by the construction of certain fundamental sets of solutions to a hypergeometric differential equation.