Exact evaluation of the Maliuzhinets half-plane function

Il Suek Koh; Yongshik Lee

doi:10.1109/TAP.2006.889966

Exact evaluation of the Maliuzhinets half-plane function

Il Suek Koh, Yongshik Lee

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The Maliuzhinets half-plane function ψ_π(z) has been used for many applications, but its closed-form has not been known. In this Communication, we exactly evaluate a known integral representation of ψ_π(z) to formulate an exact closed-form of the function, which is expressed in terms of the dilogarithm function. The exact formulation is numerically verified by comparing it with the results obtained by numerical integration of a integral representation of general Maliuzhinets function. A closed-form of ψ_π/2(z) is also obtained since it can be expressed in terms of ψ_π(z).

Original language	English
Pages (from-to)	483-485
Number of pages	3
Journal	IEEE Transactions on Antennas and Propagation
Volume	55
Issue number	2
DOIs	https://doi.org/10.1109/TAP.2006.889966
Publication status	Published - 2007 Feb

Bibliographical note

Funding Information:
Manuscript received May 11, 2006; revised October 26, 2006. This work was supported by Yonsei University, Seoul, Korea, under Research Grant 2005-1-0334. I.-S. Koh is with the Graduate School of Information Technology and Telecommunication, Inha University, Incheon 402-751, Korea (e-mail: ikoh@inha.ac.kr). Y. Lee is with the Department of Electrical and Electronics Engineering, Yonsei University, Seoul 120-749, Korea (e-mail: yongshik.lee@yonsei.ac.kr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2006.889966

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

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10.1109/TAP.2006.889966

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abstract = "The Maliuzhinets half-plane function ψπ(z) has been used for many applications, but its closed-form has not been known. In this Communication, we exactly evaluate a known integral representation of ψπ(z) to formulate an exact closed-form of the function, which is expressed in terms of the dilogarithm function. The exact formulation is numerically verified by comparing it with the results obtained by numerical integration of a integral representation of general Maliuzhinets function. A closed-form of ψπ/2(z) is also obtained since it can be expressed in terms of ψπ(z).",

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Exact evaluation of the Maliuzhinets half-plane function

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