12 



JULIUS KEAMER, 



In P kämen noch folgende von Herrn Brendel nicht gegebene Griieder hinzu : 



(24a) parsP = ^B^Xo ^v' cosmv 



+ ^Bl%';Bri' cos {mv-2Y) 



+^Bt;';'-'Rrir]' cos{mü+Y+y,) 

 +2 P:.\r ^^^'cos {mv+Y-Y,) 



+S "^n^i-i" ^VV' COS (niv — V — V J 



+ ^n}iB^,^_,^Krfsmmv +'^n}iB^\,^K'r]'r}' sm(mv+Y+Y^) 



+ '^nfiB'^^.^K'rf sin {mü+2Y) +'^n^B'^\.^K'i^'rj' sm(mv+Y—Yj 

 + '^n ^B'X.^Kvi^ sin {nw— 2y) +'^n ^ B~\,^K7)rj' sin{nw—Y +yJ 



+2 M B'"^^ . j Kr] r)'sin{niv—Y—Y^) 



+S 5:17^^'' cos (m(;+2v) 

 +S-S;'r^V'cos(w-2 



+2 niiB^.^.^Kri"^ sinnuo 

 +2 n (i Bll,^K-ri'"' sin {m\\ 

 +2wftP;l2Ä'/'sin(wM-? 



+ S"^r2.o ^"^ sinV cos mv +'^'Bl:[\'' Bsinjsinj' cos (iwt'+ü+ü,) +2 ^^0.2 Psin'j'cos m 



+ 2^«.'2.o''J^sin-icos (m(;+2ü) +2^J.\'.\'°PsinJsin/cos (m(;+ü-üj +2Pto.7-RsinV'cos(M«;| 



+ 2^;.2.7-RsinVcos (m(;-2t)) +2P;.\'r-Rsinisinj'cos(ntf;-ü+oJ +2^;.or-ßsin'/cos(«Wi- 



+2 " sinj sin/ cos {mv ~ ü — 0^) 



+ 2 f* "^„.2.0 -^sin'isin mv +2 ^«.1.1 ^sinjsin j' sin {mv + b + ü J +2 -^„.„.2 ^Tsin 'j' sin?!!? 



+ 2 ^K.lo -S^si^V sin (w + 2ü) +2 ^ jtt i sin j sin/ sin + ü - +2 ^ ^«.0.2 sin' j' sin(iiif ^ 



+ 2 f*^«.lo -^sin'i sin - 2t)) +2 Ksinj sin/ sin (w?^; - ü + 0 J +2 B-^.^K sin" f sia{m 



+^^11^ B~\,j^Ksinjsinj' sin{mv—'o—t}^) 



Die Werte der i?-Koefficienten sind: 



731-0 

 -^».2-0 



— ^ Pn-3-0 2w'^fi P«.i.o"^^-^(K.i-0)i-o 



-^«•2-0 



4 {Pyi-l'l-o 



"t~ Bn+l-i-0 



^+2.1.0 





"xj+2-1-0 



-^«•2-0 



iP 





TD— 2-1-0 

 -*-^«-2-0 



= t J'„.3.o-2^^^tP„.2.o+(w>'+|w^*)^'«.l.o 



P~'-'-" = 

 ■^n-2.0 



i P 



4 n-i-i-o 



4 



■p+2-1-0 



= -P«+i.2.i - 2 (w + 1) P„+i.,.o + wfi P„+,.,., - 2w (w+ 1) P„+,.,.„ 



"tj-1-2-1.0 



-^«■1-1 



— IP 



2 n-H-i-o 





T5+1-1-0 

 ^«-1-1 



= P„_,.,., + 2 (« - 1) P„_,,.„ + n^i P„_,,, + 2« 0?- 1) u P„_,.,.„ 



^^■fl.l.O 



-^n-1-1 



•J- P 



2 n— i-i-o 





U-M.O 



= A+1.2.1 - 2 («+ 1) P„+i.2.o - n^i P„+,.,., + 2n {n+1) (i P„+,.,.„ 



•;^-i.i.o ^ 

 -^ji-i-i 



2 n-H-i-o 





2-2.1.0 



= -P»-i.2.i + 2 (« - 1) P„_,.,.o - «f* P„_,.i,i - 2n {n- 1) fi P„_,.,.„ 



"Ö-2-1-0 



— i P 



2 Jl— l-l-O 





JßlO 

 -^«•0.2 



-^«.1.2 ~ 2-^n.i.i~ ^'^'-Pn.i-o + 2 P,„.j.Q,(|.j 



-^n-0-2 



i {Pn-l-i-o 



+ PfH-M-e 



-0+2-1.0 



= * ^"«+2.1.2 ~ + ^"«+2.1.1 + (■'^■'+ T + f ) ^"«+2.1.0 



Bn-o-l — 



i P" 



4 n-H-l-O 





jg-2.1.0 



= i- P„-2.i.2 + {n- 1) P„_,,,., + {n'-^ n + f ) P„_,,„ 



-^?l-0-2 



iP 



4 n-l-l-o 





