EVOLUTIO ^U^CTIOKlS PERTURBAIRICIS EIC. 271 



(43) ~ |sin(r^2x)— sin/j ; 



alter vero fiet 



(44) — S aa' BO)cosij-cosxcos(r-*-x)=\ 



"^ J -t-oo 



f -^i 2 aa'B(')sin(«.»-1 ]y 



et factor aequabitur quaatitali 



. ^S aa'B('-')sin(«rH-2x)l 

 a ( ) ^ -'^ ' 



(f^) — sin(j-^.2x) - sin — < 



^— ^S «rt'B('-<)simj 



—00 



26. Si in primo termino factoris quadrati p (D) loco 

 cos'O' -H a: ) substituetur ^ { cos 2 ( j -+- :c ) h- 1 j , habebimus (1 5), 

 ( num 17) 



(45) — -^ ■ cos;-cos'0--Hx)=-— I cos(3j-f.2a")-f.cos(7^2a:)-f-2cos7 | ; 



secundus vero per formulam (2) numeri 1 4 erit 



4 2_^/Af0sinz>'sin20-*j?)=-| S_ iACOcos ( {i^2]x-*-2x ] ; 

 seu posito / = / — 2 in altero membro 



(4G) is2%ini7sin2(7^x)=— iS"^^(/_2)A('-2}cos { ij^lx ] : 



lertius terminus, loco / substitnto {i — 2) in prima parte al- 

 terius membri , erit (1 1 ) num. (1 6) 



( 47). ....— |S*'*a' 2B(' )cos/rcos'(7-t.x) =5 



— 12_ a'2B('-2)cos(i7-*-2x)/ 



-00 



l—\t'^_^a-^W)cosiy 



quartus denique terminus (8), (num. 16), posito, un antea, 

 ' = / — 2 , abibit in 



T. VI 35 



