PARTICULARLY THOSE OF TWO VARIABLES. 
811 
m=oo n= co 
{TYLtjC 'll 
_ R. A 
+r -(2^+l)^ COS7r j^_.( n _j_I)l} = %—0 ltO (^) . 
m=oo n—<x> F f ^ v 7/ 1 
2 2 2 (—i)*+y^ + VY«+i)^ r 2W ) («+i) s in 7r |(m+i)- + (w+4)^| 
_|_ r -(2»«+i)(«+t) g | n 7T j (m+i)^~ (w+1) 
m=0 7i—0 
= £ ? . 
m=oo co 
2 2 2 (— i)«p»y j 
774—1 74 = 1 
_ , mx . ny\ , 0 /%# m/\l 
r 2mn cos 7 tF— J-\-r~ 2mn cos 7r^——— jj 
=—^0,0 — ^o, l (y) + 1 • 
771=00 n = CG 
2 2 2 (— lypfa+Wq ”*cos 7rj(m+i)^+'r 
774=0 74=1 L [HA 
771=00 71 = 00 
• f mx 
2 2 2 (— ly+’p^q^+w y®»+V» gin ^+(^+-J)t 
m =i »i=o L L R A 
_|_ r -(2»+l)w g in 7T + 
— ^10 “^li 1 
v ). 
771=00 777= 00 
2 £ ^ ( l\« + apU + i)*^(«+$F 
774 = 0 74 = 0 
r 2(/«+i)(«+i) s ^ n + 
774 = 00 74=00 
2 2 2 (-i)* + yY 
774=1 74=1 
o 7 %$ , , 0 [mx , ?l?A 
r 2 m eos j+ r~ 2mn cos 7 r(—+“• j 
7 71=00 71 = 00 
771 = 0 71 = 1 
2 2 2 ( — l y )M+i+np(M+Wqu* r (37»+lkg‘ n 
=&i2-0o,i( x )- 0 o,i(y)+ l 
x ny * 
771 = 00 71=00 
2 2 2 ( — i)»+«+*29»*gr(»+^ y (3w+1)M sin 7r{^+(^+-|)“ 
774=1 74=0 _ L R A 
+^ +1> ” sin Trjf-(*+«!}]=*i*-Ai(y) 
• (73). 
• (74). 
(75). 
+7'- <2 “ +1) ” CO sirj(m+4)^— =5„—^ li0 (x) . . (76) 
• (77). 
+r~ a**ix»+4» s i Iln .|( OT+ i)|_( n+ i)|J = ^ 11 . . ( 78 ) 
• (79). 
+»’“’ ,9M+1, ”sm7 r |(m+4)^_^j =$ w —d iil (x). . . (80) 
(81). 
