n 



Figure 34 - Illustrating the Schwarz-Christoffel transformation. 



Let the polygon be drawn on the s-plane and mapped onto the plane of the variable t, 

 which is also shown in Figure 34, t being complex. 



The appropriate transformation is most simply stated in terms of the inverse derivative, 

 thus: 



^^=Kit-a^) \t-a^) "'...(«-a„) 



[31al 



Here K is a. constant, real or complex; a,, Oj • . • a^ are n real numbers in ascending order of 

 magnitude; and a "^ . . , "^ are another set of n real numbers. 



The powers that occur in [31a] must be made single-valued by a suitable convention 

 concerning the amplitudes. Let a denote any one of the constants a ... a , and a the 



58 



