474 Mr. X. R. Sen on Potentials of Uniform and 



Ttetp>q : the hypergeometric series is of the form 



F(a, * + i 7 ; e*) 



_ ■*(*+$) ' «(«+ix«+|)(«+f) 



1-7 1.2.7(7+1) 



Since a>7 (ry being positive), 



a «+l a + 2 



- > — — : > > etc. ; 



7 7+1 7+2 



so 



p < i+--+l(: ..)+(i±^fc±«(5,.y + . . . . 



H«-r 



when the series is convergent. 



Here Lt - = 1 ; we can show as in § 6 that V should 

 converge at least (whatever p and q may be) if 



Lt CX p 7 -M-T-»0, 



(1 -.*»). 



where c is ultimately of the order — = 



n 2 



t. <?., > 2c. 



Hence, at least outside the same restricted region as in § 6, 

 V represents the potential function for the whole external 

 space. 



8. 



In § 3 let us suppose that e is equal to zero. An ellipse of 

 zero eccentricity is a circle and the semi-latus rectum is the 

 radius. Making this substitution, we have the logarithmic 

 potential of a circular area. 



V = 7r« 2 log r = (area of the circle) x (log of the distance 

 from the centre), and the potential of an infinite circular 

 cylinder is twice this quantity, neglecting an infinite constant. 

 Similarly, from § 4, when the density varies as the inverse 

 focal distance we have V= (circumference of the circle) x (log 



