584 

 then if 



C/ii . (in 

 f 'ill = ; Ï '^n = 



we shall find 



00 CO 



t|'(,?^) =: .??— > :S «;„.?•'" and ö(,i-) = ,?•-('—') ^ />„ .?!", 







and at the same time we find A bound to the condition l^A^O. 

 This rather intricate connection lielween if? and a greatly limits 

 the number of applications with some [)ractical significance. As a 

 matter of fact Sonine gives two, foi' the third fui-nishes nothing new 

 as we shall see. 



1. Abki/s equation appears u lien in (la) we take: i|' (./•) =r 

 — — (1 > ^ > 0). \W this >f, = J . a,, = (in > 0), by which 



.T' 



c^= r(\ — /.), r„^z=0 (?/?>()) and therefore 



</0/) r{i—x) 



fart heron 



r(i— ;.) V ^ ; 



and therefore 



1 sin A.T 



Finally follows: 



.sm P.rr 1 



G[,v) = 



rr 



.1— ; 



Sidislilution of i|' and J in (la) and (li^j now gives us: 



'J- '■>' 



J' n(i) sin Xjr f* t'U) 



2. For the second applicatiou Somnk starts from ^) : 



V(//) r= 7^1 -A). •» r- J^(l-/) 2: 



so that 



c,,= r(i-/) \-^. thus a,„= r(i-;o.-7-— -^-V 



1) 



1) The factor r (1 — ■) is addel for practical reasons. 



