OTTAVIO ZANOTIT BIANCO 



(cos 6) (sen^)"' dO= P,,{p.) (1 -//) ^ dp. 



lp,^{co^0){sen6y"'d6=L 



(l-,a') ^ f?a 



= 7r 



[1.3. ..(2^-1)] [1.3... (2^-1) (2^ + 1)... (4^-3) (4^-1)] / (^^) 

 [2 . 4 ... 2 ^] [2 , 4 ... 2 w ... (2 «?, + 2t)] 



[1 . 3 . . . (2 m - 1)] [1 . 3 . . . ( 2^-3)(2^-l)...(4ì^-3)] 

 [2.4. ..(2f— 2)x2][2T4...2m . . . (2 w + 2 ^— 2)] 



[1.3...(2.?,-l)][1.3...(2^-3)(2^-l)] j 

 ^■^ ^ [2. 4... 2 i^] [2. 4... (2 m- 2) 2^»?] j" 



Si avrà similmente, tenendo della (7) e delle (2) : 

 Ìp,,icos6){senBr'"^'dQ--=\P,,{p.){ì-IJ.y"diJ. 



— I 



_ [2.4...(2w-2)2w][1.3...(2^-l)(2if+l)...(4^-l)] ) (12) 

 " [2y4...2^]'[1.3.5...(2m + 3)(2-w-l)(2w4-l)(2w-3)...(2w + 2w+l)] 



[2.4 . . . (2w-2)2m][1.3. . .(2^-3)(2#-l). . . (4?^- 3)] 

 ~ ["274 . . . {2Ì - 2)] [1 . 3 . .7(2^^') ( 2 w? + 1 ) . . . (2 jw + 2 i' - 1)] 



, 2.[2.4...(2m-2)2m][1.3...(2^-l)] 

 ^■^^ ^ [2.4. . .2ì^][1.3 . . . (2m-l)(2m+l)] ' 



Nell'espressione (3) pongo ,a. = cos^, ne moltiplico ambi i 

 membri per {s,en 6)'"^ '^ ' d 6 , ed integro poi fra e -, avrò: 



\P,,^,{cos^){sen6y"^'dO=A,_,i 



L^_, j(cos6f'-(sen^)"'^-VZ^ + ...+^, i 



{co&6){sen0y"^'d0=A,,_^, | (cos 5)^'+' (sen^)'"-^V75 / 



(13) 



+ ^.,_, l(cos6)^'-'(sen^)"'^-VZ^ + ...+^, | cos ^(sen (5)"'+'df^\ 



