444 



n—oo 



V 



l-i)" 



Leopold Gegenbauer, 



f ^CHy) Cn (cos x) _ "V 2 / 



n 



/ 2n-l 

 V 2 



n(^2M + 2v— -) n(v— l)n(^2v— l)\/;rsin^"-' J ^" 



(cosy — cos .-r)"^' <'0S-^ 



f 



? 



cos*"'-' -^ ly, («/+sin^-|-cos*i;y+/8in^ cos^'^ sin 2^ 



sin' 24- 



?„.c4,r, v.in f „.„2.r,.:„o.i, sin" 2t|;, 



+ ?i (y+sin*-^cos*<p — 2sin-|- co8^'^sin2i^ -— ^[ df d^ 



11 



(^ 



I I (cosy — cosa;)'-* cos-^ . 



n(v-l)n(2v— 1) v/'^sin'^-' ^ J" J" 



.sin* 



i¥>, (!/+sin*X 



• f 



sin* 2i|/'\ 



'-' 1^ jy, iM+sin*-^sin''i^+/sin-^siu"4'sin2t/^ ~±J "^ 



/'S) 9 „ sin' 2ti) 

 + y, ( y + sin' j- sin* '^ — / sin -^ sin' 'j; sin 2t|/ — ^> d<f d^ 



2j „ /2h— 1 



<P^;'Hy)Cl (cos x) 



n(^) 



»=" ii(^^^jn(2«+2v— ^j n(v— i)rH2v-i)\/7rcos2'-*— ^. ^o 



(cosa; — cosy/-' sin-^ 



.cos*"-' ^ Ifi (2/+ cos' -|- cos" 'l + Z cos ^008*4' sin 24' ^—^ 



+ 



.2I 



J_ /»rtO^il 



sin'2i/' 



?i (y+cos'-^ cos* 1// — /cos -^co8*'p sin 2tp 2~^/f ^'^ ^^ 



„ /2v— U 



n(v-i)n(2v— 1) v^TTCos^ 



(rosa; — cos yf-' sin -^ 



.sin*"-' i|< jy, fy + cos'-^ sin*i/;-4-/ cos -|-sin'i|' sin 2-^ — ) + 



+ y, (y+cos'-|-sin*i/; — / cos-|-8in*t|; sin 2^ 'a')] (^? '^^ 





n(^) 



n (2« + 2v+ — ) II(> — 2) n(2v— 2) \/;r sin^"-' -^ 



(cosj> — cosa;)"-^ sin f. 



..(/.tt) ^/ 9 tt) sin* 2tL 

 .cos* ''-'4' )(sin-^cos'| + /8ini^) f^ 1 « + sin'-^ cos*'! + «' sin-^ cos'i|/ sin2i/> ~- 



sin -^ cosi^- isin\j>jy, fy + siu' -^ cos* i/; — i sin-^- cos'tj; sin 2tj> a^}\ "'? -'"^ 



