1247 
et 6 we lo gm = 
— feta", (2 aa)da = — > — Jer *a"gmn(a)da 
n! n! om! 
0 0 
where the second member may be reduced by means of (7) to 
n d m 
By (—1)™ Ce = = Pj (2). 
0 m. 
Therefore we have 
i) 
WH . eee 
Pn (©) = “fo aid, 2@Yanda. . . ss (10) 
0 
and 
of > ple) i : B Bn 2 AR * 
== Ee f (a) da fe Br J, (2 Vag) dp 
0 n: 
0 0 
Now, from the equation (9) we obtain 
SOD) 65 7, (2 fe) 
0 n! 
thus | 
S= [de f: J, (2 Vad) Si (2 VP) ap, 
0 0 
or, putting 8° instead of 9 
S=2 (F(a) def J, C8 Ve) J, IVd Reh 
0 0 . 
3. This double integra] may be determined by a theorem of 
Harker. (Math. Ann. Bd. 8 p. 481), who proved that 
ae vp (y) dy f: J, (By) J, (85) rd = p(8) 
0 0 
where § represents a positive value and p($) a function which 
satisfies the conditions of DiricHLeT for all values between 0 and o. 
Putting 
y=2Va, §=2Ve, G2V2=f (cz) 
this theorem gives immediately 
Se [faa JCO, CRVARB=Sle) . - (2) 
0 
0 
