EUOLUTIO FL'KCTIONIS PERTVRBATIMCIS ETC. 



273 



(54).. 12 /A«siny-sin2(7-»-x)= -i-Z (/— 2)A(— 2)cos(i>-^-2x) ; 



ubi in alicro membro positum fail (/ — 2) loco i. Terlius , 

 termino (8), (num. 16), in prima alterius membii parte sub- 

 stitulo parittr (r=2) proi, fiet 



,-♦-00 



-t-OO 



|£ a'2B((— 2)cos(y'-K2x)i 



(55) — ^2 a'm'kosij-sin\x-*-x)=) 



-00 



—00 



-KX) 



IS a'^Bi'hoeiy 



quartus demum, eadem facta subsiitutione, erit 



-HX) /</A('-2)\ . 



( J-2 a'/ -- — \cos(ir^Zx) ) 



(56) — ^2 '^'\~n ) cos(rsin-(;--«-^)— 



/<fA(')\ 



^^-oo«'(-zr) 



Quare si ponamus 



(57) -i{ (/- 2)A('-2)— a'2B('-2)_rt' /^^^j j=P(3) ; 



cosiy 



atque ad aequationera (50), (num. 26) altendamus, factor qua- 

 diali (ji' hanc induct formam 



3« ( \ 



(w) — , ,j cos(3/-+-2j;)-4-cos(/^2x) — 2cos7 1 



-t-co ,,, -4-O0 



-1-2 PC3)cos(«/-»-2a:)-H2 QWcosif . 



29. Quil)us omnibus functionis perturbatricis R evolutio (D), 

 (num. 13) vertilur in 



m' -«».,., 



— . 2 A('.^cosir 



2-00 -^ 



(E) R= 



m -t-oo 

 -^— . 2_^M.<')ecos(/>--4-a:— «) (b) , (num. 14), 



-^~ ■ 2;^M0}e'cos(y'-Hj:— o') (c) , (num. 15), 



fn -1-00 



- — . 2 Ni')e'^cos(ir^2x—Zo) 

 2 —00 



. (d), (num. 16), 



