James Henderson 1 73 
Since I TgTj.'ei^^/'^'fZ^ = 0 only the term in will be left on the right-hand 
side, i.e. 
T, *S' c, T, e«'/-- d^= c, T,- e^^'i'^' d^. 
J - 00 1 J — CO 
Putting ^ja = y, = crc^y, 
we have — ".-^ — ^ T.,e^^-/'^ rff = cJ T,"e^y'ady 
S V'277- 
I.e. c,= — ~ - T^e ' ' ax 
a Jo B 
V27r 1 ri r/a;-_p/(^ + (/)Y^i (g-l)(g-2) f x-j^/ip + q) 
o- Vs! \/27rio IV o- y 2.1! 
2% 2! I o- ) ■■■) B(p, 9) 
^ g j/^j: + '7)Y-^ _ {s^lHs -2) /x- p/(p + qy 
a^slKK <r " / 2.1! I 
(5-l)(g- 2)( ^-3)(g-4) / ^'-y/Cy + ry)y---- _ ) a-^'-i ( 1 - 
2^2! A o- ■■■] 
dx 
(xxvi). 
The integral for any particular value of s reduces to a series of B-functions and 
so is found. 
The area up to abscissa x is generally required : 
xP-Ul - x)i'^ , 
I.e. — -r^; — dx. 
B ip, q) 
But r ""^(^^rA':' dx = Sic.rjd^ 
Jo B (p, q) J -r. \ 
V 
= o- I S (c,T,) dij. 
-00 1 
[y 1 
Now "^sdlj = 
Jo B(p,q) dx = aj_j.r,dl^-a\c...^.r. 
nj e-W 
= o-Ci -iir^dy -a,T,- cioT. - ... - ft,T, - . . . , 
J -00 V27r 
where = Cj+i , ^ — , = ac^ ^ (1 + a) - Tj - aaXg - agTs - . . . . . 
Vs-l- 1 
