Our results are always parameterless, that is, explicit functions of the problem variables found without using rays, ray equations, or ray parameters. Whenc= sinhz, we find a series solution of the reduced wave equation▿2u + ω2c−2u = 0characterizing radiation from a point source at (x0,y0,z0) in three dimensions. Ignoring the shadow region(x − x0)2 + (y − y0)2 > π2, we use formal methods to find the first three terms ofaseries for the radiation solution, beginning with the termexp[iτ(ω2 − 1/4)1/2]{sinρ/[ρc(z)c(z0)]}1/2 cschτ, τ defined by coshτ = (coshz coshz0 − cosρ)/(sinhz sinhz0)andρ = [(x − x0)2 + (y − y0)2]1/2. In all of two‐dimensional (x, z) space except the shadow region|x − x0| > π, formal methods and reexamination of Cohn's Riemann functions show thatQλ(coshτ) is an excellent approximation to the radiation solution. HereQλis a Legendre function,λ = 1/2 + i(ω2 − 1/4)1/2, andρ = x − x0. Special and limiting cases of the above give analogous results forcequal to coshz, cosz,ez, z, and 1. We obtain Pekeris' exact solutions whenc(z) =z, and the classical solutions whenc(z) = 1.