EEV. T. P. KIEKMAi^ ON THE K-PAETITIONS OF THE E-GON AND E-ACE. 265 
where ?' > 0 : 
Rr (r, ^)„=0, 
Er“^(r, ^)„=i{2(H.H')-Rm^, 
Problem i. To find (XLI., XLIII.), 
r =w+^(l+ 2 oso)-p 2 A^fl!i-l-<Z 2 + •• Om — ^h 
k=n-\-hza -\-2hlei-\- e^-\- . . €^—2n\ y 
\ 2 n, ! 2 n 
here r and n are both even. 
M=23’" ’"'’(3+2ao, So), 
M'=2^K’”'’”“(3+2a«, sA, 
2h 2h) 
^)„|, (i>0). 
E^'^‘ (r, k)„=0 
Rnr, y5:)„=p{24E'— (3-i-2a„, e,)).2^(R--'"‘>(3+2^„ £0)}-P„E-”“'(^, ^), 
, r—2n , , 2k — 2n 
where and — ^=:s„-t-s,. 
Problem k. To find E|,-'^(r, Jc), (XLII., XLIII.); 
here h is even, consequently n is even. 
k—n-\-TiZo ^h(6i ~j~^2 Hh • • ; 
and r is divisible by 2h. 
M=2..Il— (S+2a„ £.) 
R“(»', *).=2(MA^£)-2,E««>‘ ''‘(r, k)„ *50. 
R-(»-, ^).=2,E— 
Problem 1. To find E“‘(r, k), (XLV., XLVI,), 
k'^7i-\-'2Ji^^ “l“^2 ~1" • • “P >j 
here r, k and n are aU even and divisible by 2h. 
Rf {r, A:)„=i2A„-i2T(2Rr'>'^'^'+Rr'+Rf •'’""‘+Rr^‘*^)(^ k)„} ; (i> 0 ), 
2h 
Rf‘(r, ^)„=0 
Er(r, i).= i{D(!^, ^)_E?(r, k),-U'S“‘(r, *).}. 
2 N 
(C.) 
(C'.) 
MDCCCLVII. 
