On the L4 numbers and their application

The F 4 set of complex functions: F a 4 =F a 4 (a,c;x,ε a ,ρ,α), F̅ 4 = F̅ 4 (a,c;x,̅μ,ρ,α), F̃ 4 = F̃ 4 (a,c;x,ε̃,ρ,α), equation and ̃F̃ 4lim = F̃ 4lim (a,c;x,ε̃,ρ,α) is defined by means of the complex Kummer and Tricomi confluent hypergeometric functions Φ(a,c;x) and Ψ(a,c;x), and the real ordinary and modified Bessel ones, J v (y) and I v (u), (a=c/2-jk-complex; c=3; x=jz; k, z, equation,ε a , ε̅, ρ, α y, u - real; -∞ ; 1,ε̅ = 1, 0