436 



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2r;r 



Leopold Gegenhauer, 



c-, ,^... £^^_, cos (y, sin 4;:^ +^, 2/2 sin j;: 



+ -'v-i ^2. Sin ^^) dy, dy, . . . dy,,. i ■ ■ J' iVf^+nl-^lhy^^osf,) J» {\/!/l+!/l-^l/,!/,<^osf,) . . . 



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. . -J^is/yh-i+yh — 2i(/2,— ii/2,-cos fr) cos2?2y, cos2«02 . . .cos2Ho,r/yj df. . .df^ =r 



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V 



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[r[ ^" ( \/ylx-i + yl—2y2x-i yn cos y ,,) cos 2«^,, J2''(y,,+,) f/y>. = (—1)'- 2'' k- {-^^^) \/i^'S 



I I ■l 2 '''2- ■■-%,._, cos («/ 



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TZ 2ff 



cos T — — r + s ii, COS -, + . 



- £2 ,.-1 yi, cos^^ j'7y, r/y^ . . dy^r 



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[7j J" (\/i/»^i 4-i/?).-2y2X-i yt\ COS yx) cos 2wyxf75;>), := (- !)'■ + ' 2-'-i (v^^) ^r'' 



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2_,M ="2 • • • '"2. «i^li^i COS j^rpg + =-. i/2 COS ^^-pg + . . . + £2,.i/2,.+i cos ^^ , J (Zy, dy^ . . . dy,,.^^. 

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]T| J" (\/yl),_l+t/lx-2y2),_,«/2xCOSyOCOS2«yi,J2«(y,,+ l) r/yx = (_l)'"-'U2r+l)+l+,. 2-^r^r (!L 



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... Veos(2/.cosj-^ + ..y,cos^ + .,y3Cos^+... 

 + £2,-1 2/2r cos^^^) jr| J" (\/«/5x-i2/lx-2y2,._,2(/2xC0S3>x~) cos (2/<+ 1) j^^/Zy, f^i/j . . . dy-iAf). - \ (4'-r)'- (|^ 



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V / 2;r 4;!: 6;r 

 ; cos I y. COS -; ^ + ;-, w„ cos , + £„ (/„ cos -; h 



,(4r + 2V-: 



£2ry2r+i COS ^—^ j J^j J0( y/y^. _ ^ ^y..^ _2^, ^_, ^,.^c0S yx) ■/'"+' (y2,.4-l) cos ( 2/i + 1) yx'/y, ^^2 . . . f<fi/2.+i rf^X = 



=(-^M4.)'(i:?±i) 



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) £,£2- • • S2r-1 C0S(, 



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^2 • • • S2r-1 cos ^^j COS j -+ £, »/j cos 



4^ 

 '4/^+1' 



•£2,— iy2rC0S 



>^4r + 3 

 4r+l 



jTj J" (\/i/2x-i + i/2A— 2y2x-iy2AC0syx) cos2nf xdyidy^. . .dy.,.Jf,, = ^ (^"■)'' (4;:'^7i) 



