Uniform asymptotics of a Bessel-function series occurring in a transmission-line problem

Abstract

Consider the Bessel function series S( θ) = J k ( k) + 2 Σ ∞ n=1 J n+ k ( k) cos(2 nθ), where 0 ⩽ θ ⩽ iλ with real λ → ∞. We determine the complete asymptotic expansion of S(θ), uniformly valid in θ. The expansion is obtained by the method of steepest descent applied to a contour integral representation for S(θ). The result is used to establish the high-frequency asymptotics of the linear current density on a thin conducting strip that is part of a transmission line.