Coefficient of End- Correction. 139 



boundary can be made as small as we please by choosing R, 

 sufficiently great. Then 



Let 



(-—) =/0) = A+B(i-^ 2 ) + c(i--<ri/3. 



Then 



j Ap)Jo(k P ) P dp = A | J (¥)P d P + B i J o(fy)( 1--p 2 )pdp 



+o^j Q (kp)(i--f?ywpdp. 



j (kpxi-p 2 y->pdp = 2^r(v)^.. . (i.) 



or 



if vgdS = r rf* [A^ + 2B^ +C2-WT(f)^] : 



Butt 



Then 



J. 



*" + * 2^r(i > +i)r( f »+i)r(»+/.+i)- 



Then 



i (yv iS _ A , rQ)r<2 ) VB rji)T(3) 

 2*1,* an - A 2 2 r(3)r©r(«) + 2T(|)r(f)r(j) 



"^ 2T(|)r(5)r(|) + °2T(|)r(i)r(y>) 



, 2B0 J[XI)ili]r( » )_ 2 r< §)r< ? ; )r(i)r(-4) 

 2T(f)r(|)r( V) + ' 2T(i)r(^)r( v ) 



3{r(|)} 2 L + i5 + a T57j + lra)/ L JAO r4 +it50 u-;59j 



p, r(j|)r(i) 3^3 

 r(|) io"- 



* Schafheitlin, l Bessel Functions/ p. 31. 

 t Nielsen, ' Cylinderfunktionen,' p. 194. 



