154 



5) yx^mcf — y2x^sin2 r/^ + y^x^sinS^ — jH^^sm4:q> 



+ y^^^sinöf/) — .... ( — l)''-^y°x--i:^ sinn ^ = 



yx sin 9p 



yx^siD2y 



"• sin 9p — yx^ sin 2 y yx^ sin ^ sin 3 f' 



"•sin 2 9p — yx^ sin 3 9^ yx* sin 2 9? sin 4 9p 



*" sin 3 9p — yx^ sin 4 9p 



(35) : 



n 



yx sin (n— 2) 9p sinn 9p 

 sm (n — 1)9P — yx sm n 9p 



10) Verwandlung einiger Quotienten von Reihen in 

 Kettenbrüche. 



Die in 6) entwickelten Formeln bieten das Mittel^ 

 einige Quotienten von Reihen in Kettenbrüche zu verwandeln. 



Es ist nämlich: 

 fp(—S, 2, s, X, — yx^+i)— f/)(— g, 1, g, X, — yx^+^) 



= yx2.^(-g+l, 2, g, X, -yx^+0. 



Ferner findet man die Relationen 



r/)(-g+l, 2, g, X, — yx^+i)_ r/)(-g, 2, g, X, -yx«+i) 



(g=00) (g=C>C) 



= -yx(l-x2).^(-g+l, 3, g, X, -yx^+0, 



^(— g+1, 3; g, X, — yxg+i)_r/)(— g+1, 2, g, X, — yx^+i) 

 (g=oo) (g:=oo) 



:- yxlr^(-g+2, 3, g, X, -yx^+0, 

 9)(-g+2, 3, g, X, -yx^+i)- r/)(- g+1, 3, g, x, -yx^+^) 



= — yx2(l-x3).f/)(-g+2, 4, g, X, — yx^+i) 

 r/) (-S+2, 4, g, X, -yx«+i)_ r/)(-g+2, 3, g, x, -yx^+\) 



<g=00) (g=00) 



= yx«.r/;(— g+3, 4, g, X, — yxe+^), 



