386 



It is quite clear that any linear operation with respect to 



(iJ) (l)') ( V) ( '^ • ) 



^ which transforms g*" ^ — >g' also transforms y' — »y' 



Consequently, the functions y^ ' ' U, '^) and y ' (x,V) can be derived 



from y^^^^^ U,!! , /B) as follows: 



^J W(^.^; = ^^'/»^C*,r,0 . |V^^Cx,r,p}f,^f3 cf{;7^ ' ^ . ]a(,, (23) 



The functions h^"*"/^^ (x, f ) and h^^^^^ (x, V) can in a similar fashion be 

 derived from a function 



>s^Kr,^,,.<^').. r ^'^('>,c) '#"'V..,(.9 i^: 



, dx " ' >'^' ?x 



(25) 



as follows: 



6A}- '*''* 



»t^"^V^.r)c K^'^^C*,t,.,.) = 1^ J^ i,^'^-»Ur,r»,(30^(3'a(.dp; (26) 





(27) 



69 



