BOUNDARY PROBLEMS AND DEVELOPMENTS. 119 



A A 



Hen 



ce 



/,-- ~ ! (©*(* + (>) '+(«)}. 



which integrated over C M „ gives 



^/{(#')^ + o)- + w}f = |r( 5 <f»)F(x + o).+ ( e) . 



By familiar reasoning this leads to the equation 



and inasmuch as 



Z ** 



> 2s (gjf >) = i J, 



C 27T 



as may be shown by applying again the argument by means of which 

 relation (109) was established, we have 



i.e. 



(113) lim S<£(x)-=iF(x + 0)- 



TO=0O 



ui. s l 2(z)-. 



Following the procedure used in the discussion of the preceding 

 expressions, let J$- be defined by the equation 



6 



J 3 - = - Y(x) A- 1 J W a Y(a) (4*) Z{t) R(t)F(t)-dt. 



a 



Then S%(x)-= ~JJ r d\. 



Now 



A - 1= f^)) 16 

 \ D(\) '> 



16 See note on page 104. 



