@article{oai:ir.kagoshima-u.ac.jp:00010741,
 author = {MURASHIMA, Sadayuki and 村島, 定行 and KIYONO, Takeshi and 清野, 武},
 journal = {鹿児島大学工学部研究報告, The research reports of the Faculty of Engineering, Kagoshima University},
 month = {Sep},
 note = {It is well known that there are three kinds of cylindrical harmonics which are used to express the potential functions in the cylindrical coordinates. The three kinds of cylindrical harmonics have their own regions of rapid convergence and are called the z-, r- and φ-form. The cylindrical harmonics of the z- and r-form are very popular and are oftenly used in many field of physics and engineering. However, the cylindrical harmonics of the φ-form which involve the modified Bessel functions of purely imaginary order K_{is}(x) and I_{is}(x) have not been used for the analysis of some practical problems.
In this paper, we discussed the possibility of analysis of potential problems based on the cylindrical harmonics of the φ-form. Usually the expression of the φ-form is given in a series of some kinds of integral with respect to the order s. It is shown that this type of integration is carried out efficiently by a method which is a variation of the Double Exponential quadrature formula recently presented by Takahashi and Mori. By comparing the computing times which are required for the analysis of two analogous problems with non-axisymmetry, it is concluded that the complexity of this new method of analysis is the same in order as that of ordinary method using the expressions of the r-form. As an applications of this method, we analyzed some potential problems in connection with the four point probe technique.},
 pages = {133--144},
 title = {Analysis of Potential Problems by the Use of the Cylindrical Harmonics Involving the Modified Bessel Functions of Purely Imaginary Order K_{is}(x) and I_{is}(x)},
 volume = {15},
 year = {1973}
}