2] 
SYMBOLICAL EXPRESSION. 
II 
Or the function <f>(a — x, b — y...) not becoming infinite within the limits of the 
integration, we have 
ff... (f) (a — x, b — y ...)dxdy ... 
‘‘¿Ilk, ... 7T*” 
£ 
r (|n) ^°2^ +1 .1.2..._p4n(|n + lj...(Jn+jD)r da- 
the integral on the first side of the equation extending to all real values of x, y„ 
h^h- 
1 
0C~ f lï~‘ 
&c., subject to -t^ + To+ ••• < 1. 
Suppose in the first place <6 (a, b ..0 = - 
F V (a 2 + b 2 ...f n 
By a preceding formula the second side of the equation reduces itself to 
2hh,... 7r in f 1 a?” -1 dx 
y being given by 
Hence the formula 
r (in) J o V{{rf + h 2 x 2 ) {if + h 2 x 2 ) ... (n factors)} ’ 
a 2 6 2 
if + h 2 rf + hf ’ “ 
dxdy... 
... n times 
2hh,... 7r in f 1 
{(a-tf) 2 +(£-y) 2 ... } in 
¿c n 1 . dx 
r (in) Jo VK 7 ?' 2 + fdx-) {rf + hfx 2 ) ... (n factors)} ’ 
where the integral on the first side of the equation extends to all real values of 
x, y, &c. satisfying j- +y- + &c. ... < 1; if, as we have seen, is determined by 
a 2 b- , 0 
^+^ + ^+^ 2+&C - -1; 
and finally, the condition of <p{a — x, b—y...) not becoming infinite within the limits 
a- b' 
~hr- + h: 
of the integration, reduces itself to ~ 4-... > 1, which must be satisfied by these 
quantities. 
Suppose in the next place that the function </> (a, b...) satisfies + &c. = 0. 
f d 2 \ 
The factor f/¿ 2 &c.J may be written under the form 
+<*«■ ~ ^ +&c - + » (i + m ■■)=<*• - ,i!) w +&c - 
2—2