140 Scienze 



e quindi 



/'^ scn»"9dy jz / (1. 3. 5.. . 2n— 3)A'l"-' 



" 1 — wi^ 4- m^rsen^9 ~ 2F''sen'e V 2. 4. 6. . . 2« — 2 



( 1. 3. 5. . . 2ra — 5)ifc^("-' ) (1. 3. 5. . . 2n — 7)A'('*-3) 

 ~~ (2. 4. 6. . . 2« — 4)tang^9 "*" (?. 4. 6. , . 2n— ejtang'iQ 



cot2(''-')cos5 



icot^C-'lSip 



[/■(l — A'^sen^S) 



) 



II doppio di questa espressione rappresenta la derivata 

 dell'integrale H^n relativa alla costante m, perciò abbiamo 



dU;.« rr /(1.3.5...2n— 3)AM"-') (l.3.5...2n— 5)A;'>-=')cos*9 

 "dm" ^ Ìfc^A(2.4.6...2n — 2)sen^? "" (2.4.6...2/Ì— 4)sen49 



(1 .3.5....2n '- ?)A»("-3)cos49 cos'I"-' )9 



"^ (2.4.6...2» — 6)sen<^5 " sen^''^ 



cot^^-'S V 



sen5l/'(1 — F'-sen^S) ' 



dunque naolliplicando per dm := cos0d5, ed integrando 

 si trova 



__ TT / (1. 3. 5... 2ft — 3)^^1"-' ] fcosUQ 

 ^"~M 2. 4. 6... 2» — 2 -^ sen"5 



(1.3.5...2n— 5)/t*(»-=') rcos^eàB (1.3.5...2ra— 7)H"-3) /^ cosSgdg 

 2. 4. 6... 2n — 4 -^ sen49 "*" 2. 4. 6... 2n — 6 J sgd.^9 



/cos»"-i5d9 __ /■ cot'"gd9 \ 

 S)en^"9 "*"*/ [/-(l — k'seuW 



