Uniform asymptotic expansions for hypergeometric functions with large parameters IV

作者：Khwaja S Farid^*; Daalhuis A B Olde

来源：Analysis and Applications, 2014, 12(6): 667-710.

DOI：10.1142/S0219530514500389

• Gauss hypergeometric function
• uniform asymptotic approximations
• Bleistein method

In this paper, we obtain asymptotic expansions for the Gauss hypergeometric function F-2(1) ((a + e1 lambda, b + e2 lambda)(c + e3 lambda); z), where e(j) = 0, +/- 1, j = 1, 2, 3, as vertical bar lambda vertical bar -> infinity. We complete the results of three previous publications [Uniform asymptotic expansions for hypergeometric functions with large parameters I, Anal. Appl. (Singap.) 1 (2003) 111-120; Uniform asymptotic expansions for hypergeometric functions with large parameters II, Anal. Appl. (Singap.) 1 (2003) 121-128; Uniform asymptotic expansions for hypergeometric functions with large parameters III, Anal. Appl. (Singap.) 8 (2010) 199-210], discuss all cases and, what is new, we consider now all critical values of z. For one case, the full details of the well-known Bleistein method are given, since a new technical detail is observed.

• 出版日期2014-11