ALCUNI TEOREMI SUI COEFFICIENTI DI LEGENDKE , 21 





log l — ^^ ^ r, (a , .X UZ u. d Q 



y \ ^ u . ' ' ' ' I seguito 



(48) 



^r,(i)j;p,(a) 





/+1 '^ '/ ' '^ '^ ' 0-+l)(2/ + l) 



IX. 



Se nelle formole (16), (18) e (19) al paragrafo IV pongo 

 r := , esse divengono : 



|P,acos5)(cos5)"f7^=j P,,(,a)(/a 



O — I 



1 e \rHtx'-if' , du. 

 4'. (2 0! / du.^' ^' ' \/Y^' 



d[j. 



yi-p.^ 



_^j [(4^-l)(4;^-3)...(2^+l)][1.3...(2^ + 2^-l)] } (^9) 

 ~^ I [2.4... 2^] [2. 4. 6.. .(2^ +25)] j 



[(4^-3)...(2^-l)ì[1.3...(2^+2g-3)] 

 [2.4...(2^— 2)x2][2.4...(2^ + 2i- 2)J 



[1.3...(2^-3)(2f-l)][1.3...(25-l)] ( . 

 ^ [2.4...2^][2.4...(2r+2 5)] j' 



I P,,^ , (cos 0) (cos 5)^^75 =ÌPu-,, i!^) (P-) 



O — 1 



1 f^'d''^'(u.'—ì)''^-' , r/a 



2^'+'(2^ + l)!j d^'+'a ^'^^ ^'- 



d fJ. 



