46 



Art. 7. — K. Terazawa 



4-a/i./ l A-V- J 



) (99) 



Ta/j. 





The integrals contained in the above can be obtained by 

 expanding the trigonometric functions into power series of k and 

 making use of the formuke (42). In this way we have 



u, = 



_M_ ^_ y( i)n-i nj-ln-^)] ( a \^---' \ 



2-a/. • VrH/„4/ ' [%i + \)\ \ Vj^+¥'I "■^^- 



2</i + ^) ' V,---' + r^t\ (2« + 1) ! ^ Vr^+^/ '""'^ ^' 



^ = A^L ^ ^/ nn-i ^K2»-l)! 



2.Ta/i Vr' + ^' n = 1 (2m + 1) ! ^ V*-- + ^' 



•2n-\ 



P.n-l(>) 



):ioo) 



_^ 3//(>t + 2/z) 

 Avliere 



^+^U ■ (2m+1)! lvr^+7^/ ""^^j 



*> I 5 



Vr^ + 



These series converge for Vr^+;?'>«, and are apphctible in this 

 region. 



At the boundary, we have to put z = and v = 0. Since 



Pô\o) = h PL.Xo) = o, 



2.4 (2n — 2) 



1) For the first term (h = 1) of tlie second series we have to take — ;- P-l ('y"). 



