Abstract
Mathematically, M (ω, ξ)=0 means a mapping of one variable on the plane of the other complex variable. In this stage, no physical condition is involved. At first, a technique of calculating complex variables is described. Using supplemental parameters Θj′s, wave numbers ηj′s in vertical direction can be easily investigated. Multi-valueness of ηj is attributed to arbitrary selection of mj even or odd. Next, explicit expressions of ω and ξ are obtained which contain only another complex variable γ. Some arbitrariness of m2-m1 has been related to orders of modes due to multi-valueness of trigonometric functions. Preferable RIEMANN sheet of mappings should be chosen in future by considerations on physical conditions.
