The asymptotic expansion of a hypergeometric function ₂𝐹₂(1,𝛼;𝜌₁,𝜌₂;𝑧)

Abstract

The asymptotic expansion of a hypergeometric function 2 F 2 ( 1 , α ; ρ 1 , ρ 2 ; z ) _2{F_2}(1,\alpha ;{\rho _1},{\rho _2};z) is given in terms of hypergeometric functions 2 F 0 ( z − 1 ) _2{F_0}({z^{ - 1}}) and 3 F 1 ( z − 1 ) _3{F_1}({z^{ - 1}}) .