Uniform asymptotics of a Bessel-function series occurring in a transmission-line problem
Jolanda Boersma · TU/e Research Portal · 1990
Abstract Consider the Bessel function series S(θ) = Jk(k) + 2Σ∞n=1Jn+k(k) cos(2nθ), 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.