( 349) 



r*(2 — 2u) 



/"■°°. r (2 — 2m) 



g-r(cose + «uB) r-2u+l dr =z 5 : ' (« < 1) 



,J (cos 8 -\- sin 8)-~ 2 " 



therefore 



J' 2 (.sin 8 cos 8)'" 



cos (vlg tg 8) \ ' d8 



(cos 8 -f- sm 8)-~- u 



n (sin 8 cos 8)-" 



M< + N* = 2r(2- 2u) cos (vlg tg 8) \ ' d8 . 



K J (cos fr -\- sin a)-~- u 



If in this integral, we change the variable by the substitution 

 tg 6 = <?~ 2 < 

 it takes the form: 



M* + tV 2 = 4 T(2— 2 





cos (2rt) dt 



'« it ~~T~ C I i 



!+e -*)2-2« 







With this value we find 



4;rr . „ x ,„ „ „ r°° cos (2c/) .It 



— = 4 r(2 — 2m) (e2"" — 2 co.s 2 jtm -f e~ 



and finally 



C0S(2r/),// 



» / r 5 \ r»r(2— 2 M ) r 



77 X + FTÜ )= „ V"'-2«» 2,-im -f e - 2 -) - 



= uV («*+«)v * J( 



(g(_|_ c -«)2-2« 



which holds for all values of r, and for values of u between and 1. 



2 1 3 



It for instance we put v = — , u = - and - we obtain 

 2jt' 4 4 



( 1 + £X 1+ ^X 1 + ^) 



r 2 ( - ) r( - ] « cos| - | rf« 



'J <«<+«-)< 



and 



fi + ^Yfi+üLV 1+ _*iy.= 



V 9jt 2 7 V. 49ffV V 121*7 





J («' 



+ *-<)* 



23* 



