238 
2°?—] 27—] 
1-a,).(7—*\4a-aye. (2), 
abe. (7 sa-aye (= 
For the evaluated result, Binet has obtained the very simple form 
are F (p,q). 
(5.) To evaluate the integral 
|) @-) 0 -a)'de 
0 
quoted by Haan from Lobatchewsky, Mém. Hasan. 1835. 
It is obviously equivalent to 
1 1 
_7\0 b + — rye pes 
(-1)'a , (; {, @-2)'a (1-2), 
+1 
or, finally, 
or, at once, by a previous example, 
1 
(a+1)(a@+2)...(a+6) 641 
The form in which the value of this integral is given by Haan is, in the 
notation of Kramp, 
eee L 
gutn 9b? 
the law of this notation being expressed by the formula 
am" = 0 (a+mn)(a+2n)....(a+m-—I1n). 
(6.) It is a well-known theorem, due to M. Dirichlet, that if the vari- 
ables x, y, 2, &c., be connected by the condition 
xt+y+s+&e. £1, 
then will the multiple definite integral 
[[[---2Pymen.. dedyds...= EE) Ei ae 
TV(l+limt+nt...) 
Hence it follows that, if ® be any algebraic function, the symbolic reduct 
form of the result of the evaluation of the multiple definite integral 
(proposed for discussion, Moigno, Legons de Cal. Diff. et Int., tome ii., 
p. 265), 
(Jf. -- B(wtytst &e.).ctymerl., dedyds... 
is simply 
T(1)V(m)T (mn)... 
® (6714 €Pim + €Pn + Ke.) . f 
( ) V(itli+mint+...) 
