Real-Argument Incomplete Hankel Functions: Accurate and Computationally Efficient Integral Representations and Their Asymptotic Approximants

Novel accurate, computationally efficient integral representations of the real-argument incomplete Hankel functions of arbitrary order are presented, leading to a straightforward numerical implementation. These representations are shown to yield analytical approximants, expressed through known special functions, which are also accurate and valid for any arguments of the incomplete Hankel functions. Through these representations, the electromagnetic field distribution excited in planar and truncated cylindrical structures can be determined accurately and efficiently. Numerical results based on the exact and approximate representations are presented to demonstrate the effectiveness of the proposed integral representations in the analysis of the electromagnetic field distribution excited in complex structures.