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).
Bibliographical noteFunding 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: firstname.lastname@example.org). Y. Lee is with the Department of Electrical and Electronics Engineering, Yonsei University, Seoul 120-749, Korea (e-mail: email@example.com). 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