±68 Mr. N. R. Sen on Potentials of Uniform and 



ellipse. Proceeding exactly as in the previous case, we 

 have 



V = F+2 f * COSq^d^_ 



_ V r+P+2 f * c_osjfcos^(H)4 



= P +g f eos^# 



(p + 2)J- ir (l+«COB0)' + » rt 



^ 2n"Cw + » + 2 , )r w J_^ (l + <? cos<6V + P+ a 



and substituting the values of the integrals from § 2, 



V \P+ 2 ™ \n+P+2 , Kn+p + 2 //.» 



loo- r 



IT 



p+2 (p + 2) & tf 2n(n+/> + 2) 



^ 2><(n + v;-f2) \r / 



where n^q is the positive value of the difference between 

 these two integers. 



When q—p one half of the series is expressible in a 

 simpler form; since 



A n +P + 2_ ( 1 ,n+p (2n + 2]) + 1) I <?»+* I 



■ 2.(2p + l)l 



jo! (p + 2)! lo S r 



(n+p + 2)l (« + />) !"2"+p- i '(i_^)»+p+«' 

 this part of the potential function can be written as 



(-iyy 



2 p (l-e 2 ) p+ * 



3/ 1V , O + gy + 1)! /«\» -i 



the other part being expressed in hypergeometric functions. 

 This is possible only within the limits in which such sepa- 

 ration of terms is legitimate. A similar simplification is 

 possible when q = p + l. 



When 2 = and <r = p p the potential is given by 



n = l 



It may be noted that when p is a negative integer this 

 formula is applicable with a slight modification. The terms- 

 beginning from the first up to the nth where w= — p + 1 



