490 
ee se ue 1 
tls ) = 
hit sie ae er te = zi fray — z ff voo dy . (1) 
0 0 
By writing in this formula f (4) = y" (1—y)", we conclude 
(| fy ee Poets ayes ee ) eee 
21 221i 271 Ini ik 
PA De 
0 numint 
ze nn + I, (m,r) 
for m and » integer and positive and by giving deale values 
to m and n, in this relation we find for § (3) 
2 A Ja” 23° 
=— I, (2,1) =— J, (1, 2) = — — 7,68, 1 — I, (1,3 
I= N= ADE LEDS 5013) 
If, however, f(y) represents a polynomium in 4, which disappears 
for y= 1, but not for y=0, formula (1) will hold good if f(y) is 
replaced by /(y)—A—y) f (0); this produces 
1 
= — xi it fy) — (Ll — y) FO) dy + 2 f f(y) — (L-—y) f (0) cotg ary dy 
0 0 
i l 
1 
45 nif ry dy + 4 ai f(0) — oe € — A coty ny) dy +- 
| 
Ahm of — v2 cotg my — oe „foo dy 
a J dy-+-4xif(0)- | von) nn OEL Vay pf (O)log2a. 
The particular case / wy = (1 — y)" pr sane the formula 
zu Ne ze 
eeen 
dj AS 5 Se Tega) HS 2a 
we. for n= 
Qn? (11 
ee eg Oar (ely 
Dawes oO 
