1203 

 a 



we have 



Lim -^ e '''(7^=-—. e ''' d^ = i 



. 



Ill the same way the value for .i' =: 1 may be found. 



SECOND SECTION. 



9. Considering the functions 



(pn (x) = Qe 2 ff^^ (.^) 



and determining the vahie of the constant d so that 



00 



(x) dx = 1 



we easily get 



and 



C„r= 



2 2 \/n! l^jt 



1 -- 



2 2 j/^/l3/,^ 

 Putting these values in the integral equation 



00 



(fin («) = K 1 <^H («) ^ ('^1 «) f^« 



— ■ 00 



we shall now determine the unknown function K{j;,tt) and the 

 unknown constant A,j, which verify this equation. 

 The expansion II from Art. 8 gave 



An = —— — e- (-,5;. H, [a) da = '- 

 2».7i!yjgJ n! 



00 



thus, changing ^ into u, 



00 



(2^0" = -7= P" '-^"^ ^n («) da. 



