EVOLUTIO FLNCTIONIS PERTL'RBATIVICIS ETC. 269 



.-+-00 /dXi')\ 



(35) — iX rtl— — |cos/>'sin'a:=< 



^ -cc \da I -^ ) +00 /JA(0 



^+00 /dAi')\ ,. „ > 

 -oo \ da / ^ ( 



-t-oo /dM')\ 



-i^-ooi-d^Y'^'^^ 



Hinc posito 



(36) ij iA(')-,.a2B(')-wr/— \ j=PC'); 



atqiie coefliciente Q'"' (32) ex nuraero 19 hue revocato, factor 

 quadrati q evadet 



-t-oo rt-CO 



(m) £ cQs(ir-^^2x-t-X Q'<')cos/r . 



^ ^ -00 ^•^ -00 -^ 



22. Primus terminus factoris producti /?/^' per formulas (1 5) 

 numeri I 7 flet 



ft 



(37)..... ^ . cosj:cos(j*ar)= — ~ [ cos( j*2j:)h-cos7 } ; 



pariterque secuudus erit 



-1-00 



-■*-oo 



^^S «a'B('')costycos(/^2x)j 



E aa'B('')cos/;'cosj:cos(j--»-x)=< 



-00 



-HX> 



^S aa'B(')cos(7'coy 



-co 



atque ambobus his terminis per aequationem (3) numeri 14 

 versis in formara accomodatiorem, et dein mutato i in (/ — 1), 

 eril etiam 



"*"00 "\ / -+-00 



iS_ aa'W)cos[(i-t.1))r^2x)]l \ i'^ rta'B('-i)cos((;-.-2.r) 

 (38).. _ ^^ ^'^ 



-00 



Quare factor product! pp' evadet 



hOO 



a ( ) 



i^_ aa'B''-i)cos(iy-*-2x) 



-co 



(n) cos(/^2x)-Fco.y ^t- 



42 aa 'BC'-i)cos/r 



•^ -CO -^ 



