326 
g, (t). Further, we may notice that w(tqy) and y~™ (tqy) vanish when 
tx, and that 
h meefih 
IkH ( — el) — 9k+1 (0) = (— 1)k+1 Fre (-) 
where /; denotes the Bernoullian polynomial of order 4. 
In this way the equation (6) leads to 
n ee 
> k=2m—1 
plngy + hy) — & (ng = Tile, ‘p)=— ro “i Batti \ p84. 
In this equation we have 
t a hp 
g Y= 3 BE kt 
NE 
() (0) == (+) (Di) cot v) Ld mhp 9 
ape 
and the remainder integral A is given by 
“a 
R = j— gem vn | 
0 
Now since 
h 
dom ( Es =) — J2m (t) | g (3m) ( q y) dt. 
q 
k=+a 1 
(2m) ¢ Den DL = =e 
pen)(t g 1) << 2m ese mes S 
k=+n 1 1 
2m! = 
TENCO Bak 
we infer that 
R\<2\gem (0)| 2m! g2—1 2m ait tl Mei oa 
Te er Coherence 
or that 
RIS me | ga, (0) | gt layer gE (Oe 
Thus it is shown that |# is less than a finite multiple of the 
modulus of the last term in the sum that precedes, and we have 
found the asymptotic expansion 
ht (iN he An 
Ti, («,p) = = (-) gl log— frl —](D cot) rip + 
an k=0 2 EE q = 
1 \2e—1 
a Kym ( og =| 8 
& 
where the value of is finite and independent of «. 
Putting 
h==q—1 
h 
Ag == > Tk (=) (D® cot») _ aps 
il = —— 
q 
