266 REV. T. P. KIEKMAN ON THE K-PARTITIONS OF THE E-GON AND E-AAC. 
Problem m. To find Jc)^ (XL VII., XLVTII.) ; 
here n, h and r are odd numbers. 
r=n 
Jc=^n — “l“^2 
Rp’”" (r, ^)„=2A^— A:)„, (^>0). 
‘ 2A 
Rr“ (r, ^)„=o 
Tiju, 7\ -T^/Sr + w ^k — 2n\ 
Er-Cn %=d(^-2^, 
Problem n. To find Ro-’”®(y, A:)„ (XLIX., L.), for n odd and n even, 
^=w-|-AgQ -j-2A/6j -|-^2 “h • • "b 
\ 2A ) 
H=2„,{2R-“^(4+2ao, go)+R^'”“^'^^(4+2a„, g} 
R^“(r, ^)„=2H.A^-2i.Rf''+^’’"'’(r, (i^O), 
2A 
when n is odd. And, when n is even, 
T — • • ~t~ ( ln—2h\ •\-}l(X,n 
V 2A / 2A 
w-j-Aso -|“2A(^i -|-^2 “b • • “b ^’*~2 a\ j 
V “SF'/ 2 A 
H"=2,(2E"<'+E*'“''*^2+a., 
M=2.E”“"(3+«., £,); 
E{ •”(»•, A),=2(H»M.A._,.')-23»+»» -”(!-, k)„ (*50), 
\ 2A / 
Rr’^'^Cn ^)„=2,„|(2R-“^+R^““^‘'')('^,^)| (w odd) ; 
Ro’"®(r, A;)„=0, for % even; 
Rt””'®(r, ^)„=2H"M, if I be odd, and =0, if | be even. 
Problem o. To find R^“^‘*‘(r, k)^ (LII.), 
^)2=2,2:„{Rf 
Here r and k—1 are both even, by Problems b, c, as well as n. 
Problem p. To find k)^ (Llll.), 
^)2=SAS„{(2Rf“''+R|f +Rf“^‘^'+R^“^'^‘)(r, 
Here r and k—\ are both even (Problems b, c, k, 1). 
Problem q. To find R*’(r, k)^ (LIV.), 
R‘''(r, ^)2=2,,2„Rf +‘>*(r, 1)„. 
Here r and k — 1 are both even, by Problem 1. 
