438 



Leopold Gegenbauer, 



:i TT 



11"+%^ 



2kTi 





(-1)" 



+1 



14175;: 



4n 



21 



ll'!4— 



'oo /^oo / oo 



/O ^0 JU JO E 



2_^t^ sj . . . £.,._i COS i^jy sin ^-^ + £,^2 sin 



4r+l 



. 2r;r n 





oo /^ oo /^ oo /•tt /^tt 



I ■•• Ijih- ■ ■ '-^r Sin ^y, sm^-^^ + £,j/, sm^^:-^ + ■ . . +e,,y,^+, sin ^^ _^g^ 



r 



■ Kl -^^ (\/yix-i+i/2x-2y3x-iy2xCOsyx) -^' ' '^^''\yir+i) cos (2>'+'3i'-5'y^) %,c/y2 . ; . di/or+idfx = 

 1 



= (-l)'-+^.(^+')+4^'] +^['4-1(4;r)'- \/4m=^ 



OO /* OO /^oo 



[ I ( ■••( y =-,£,.. --.._! cos (y,cos^^^ + s,y, cos ^ + ...+c-,._.y,. cos ^). 



r 



. 171 J" (\/«/Ix-i-H</2x— 2«/2x-iyäx cosyx) eos (2'-.+' 3i^5^ yO f^yif^i'a • • • (ly-i,dfx = 

 1 



•oo /*oO /*oo 



*oo /*o0 /^OO /•ti /'ti 



I ■•• lM-^.----'-sn,(y,coSj^:^+.,2/,cos;j--^ + ......_,2/,.cos^^-^). 



J(\ Jo Ja £ 



. O -^"(v/y'x-i+i/lx— 2!/2x-ii/2x cos yx) -'''"' ^^^\ll2r+i) COS (2^i+'3!^5'' yx) dijidy^.. .di/-.r+idf, = 

 1 



^(_i)^Vx,+.(x.+i,+.[^]+.,[^4-^]^4^^. 



4rn' 



f °° r r r V / 2;^ 4;: 4. 



|7[ J" (v/ylx-i +i/lx - 2yr>.-i yz,. cos j,,) cos (3>^5" y>,) rf//, (%2 . . . dyzrdf, = (- 1) '■ t^^^ + ' t^l 2^-' /r" 



•oo /■ oo /"oo 



)^ J^' J" Jo Jo J» ^ 



\' / 2k An (4?-+2)7T 



> C0S(M. cos- -+£,W2C0S;, TT +■••+ S2,-«/2r+l cos — ~ 



-j V' 4r+3 '-^ 4/- + 3 •' 4r+d 



• TTf J" (s/ylx-i+ylx— 2y2x-iy2x COS yx) J*''^'+ ' (^2^+1) cos (^6v■b■'f■^dy^ dy^ . . .dyzr+idfx = 

 1 



