ME. W. H. L. ETJSSELL ON THE CALCULITS OE iTJNCTIONS. 
266 
we shall have 
Let 
then 
Let 
then 
and 
Now 
<p,{2z)—a<p,(z)=z'FS^^^-{-^ cos 
^ 
(2^*) 2^*1' 
(^2^ — ?(j^ 2 ®+*^ ~\~^ %^ 2 ''+ 3 ^ "f" • • ' “ 1 “ «o+i’ 
C’' (xif)+x{^~’^))d^ _ 29r 
Jo 1-^ 
■2«cosfl + a^ 
whence (a) is less than unity : then if 
gfaj — . ^P + W+l 
and 
also 
we shall have 
»=(«+!) log,2+mlog,2, 
Ai)=iin+-xh-'% 
Md§f{6) . sin {f log, 2'’+*+w^ log, 2} 
+ • • . 
=-r” 
’^Jo Jo ^ s-e-s-’^f 
{ sin (§ log, 2*’+ ') + « sin log, 2'’+' log, 2) + a" sin log, 2"+" + 2f log, 2) + &c. } 
= - f ” d6d§f{ 6) • + . sin (g log, 2^+0 — « sin (g lo^, 2”) 
’^Jo Jo 
g'^? — £ 1 — 2 « COS (g logs 2 ®+*) + a® 
Hence 
g(jr— 0 )^ _|_ g-(n— fl)e 
e'^? — e-"S 
in I § logs 
COS" 
2rx — n I 
COS" 
2rx—n I 
1— 2 acosJ glogs 
1 
COS" 
2rx — n 
/ 
+ a® 
J C logsOt 
' / ,2rx—n\ logsi’ 
I r»Ae — 1 \ O 
/ , 2rx — ra\ 
(^cos-«-^j 
