146 



X 



^W==^ f{^^)e---du 



or 



The general term in the series of the second member being 



00 — X 



it is obvious that for }i = 2k the imaginary part and for « = 2/(' -|- 1 

 the real part of this integral vanishes. Thus for ii = '2k 



00 



F.2k — 1^2" fe-^'IIok (v) cos [l V 1^2) dv , 

 where according to Art. 8 II 



thus 



2k-\-l >2 



P2k — {- 1)^2 ' l/jl^g '' ;i2fc. 

 In the same way, we get 



and therefore 



e 

 F{k) = 



= - e ^ [-S (- 1)^ C2k '^^^ — i ^ (—1)^ C2k+i /2^-+'] . 

 In the same manner we find 



«P (;i) =r =:: e * [2 (— l)^' 60^ X^^^ — I ^ (— l)^' 6,jt+l P-^^+l] 



and finally 



