and then
| dΩ | = − | 1 | √ (b − a′·b − a′) | , | dw | = − | m | , | |
| du | 2n | (u − b) √ (a − a·u − a′) | du | πu |
(10)
the formulas by which the conformal representation is obtained.
For the Ω polygon has a right angle at u = a, a′, and a zero angle at u = b, where θ changes from 0 to ½π/n and Ω increases by ½iπ/n; so that
| dΩ | = | A | , where A = | √ (b − a·b − a′) | . |
| du | (u − b) √ (u − a·u − a′) | 2n |
(11)
And the w polygon has a zero angle at u = 0, ∞, where ψ changes from 0 to m and back again, so that w changes by im, and
| dw | = | B | , where B = − | m | . |
| du | u | π |
(12)