491 
If we reduce the height of the rectangle to half its original height 
and so take it equal to zr, we find in the same way as in which 
(1) has been deduced, supposing f(y) is a polynomium in y dis- 
appearing for y = 0, 
pe Daf Ge Djinn fina: from 
e2— | 
aaa as: 
zitt) 2 it! }rw0 
ze Er ene ema 
e+ 1 a e+] uae | 
0 0 0 
=/ (1) lo + fy ets A0} Ps fe NS Sal gee 
a q En : eer ee | ean Big 
(0-9 
tt 
f (1) log 2 +f Sa de 
Ee 
at last 
1 1 
LON . B Crans RY 
AE || f(y) dy — fl) log 2 + J F (y) cotg dy - (2) 
u 0 
The substitution f (y) = y" (1—y)" produces the relations 
Zim zi cu \n zy \m zi \N 21 \m 
Oe di Ee GQ eet ee dn 
DENDE Ee), 
: - dz 
zuim; In! in. N 
= — m,n 
2(m +- n BE 
for m and „ integer and positive and 
zi in zi m 21 m 
of — | +{ 1+— } —| 14+— 
4 JL 20 mM : 
f~ pf ars GEER Oe d 2 + I, (m, 0) 
Co = = log 
er] 2(m-+ 1) : 
for m integer and positive and consequently in particular 
