( 401 ) 



CHAPTER XXVIII. 



MISCELLANEOUS PROPOSITIONS. 



369. IN the present Chapter we shall investigate various 

 propositions which afford valuable illustrations of the prin- 

 ciples of the subject and lead to important results. 



370. The following formula is due to Jacob! : 



d n ~ l (1 - a; 2 )""* _ , ^,^1.3.5... (2n-l)sinnfl 



dx n ~ l ~ ( l) n 



where x = cos 6. This we shall now demonstrate. 



Put y for 1 cc a : we have 



thus by Art. 80 



Also 



dx ' dx" 

 thus by Art. 80 



cw 

 From (1) and (2) by eliminating ^_, we obtain 



T. D. C. D D 



