470 Mr. N. R. Sen on Potentials of Uniform and 



in comparison with other terms the potential is approximately 

 given by 



7Tl P+S r..+» a .+81 sin ^ 



V = -^T3)W«7 



hence the corresponding equipotential lines are arcs of 

 circles touching the major axis at the focus. 



We can determine all the cases in which the hyper- 

 geometric functions appearing as coefficients in the trigono- 

 metrical series are expressible in finite forms. Two cases 

 we have already studied where thoy reduce into binomials ; 

 let us inquire if in any other cases such reduction is possible. 

 The function F(a, /3, 7; c 2 ) will be a binomial expansion if 

 either y = u or y = /3 *. Taking the most general case, (i.) § 4, 

 we seek to satisfy either of these conditions in both the 

 functions A"+£ +2 and AZt p q +2 by giving suitable values to 

 /> and q. 



hence for the required condition we should have 

 n + q -f 1 = either n + 1 +^—^ 



, 3 , p+q 



i.e. p = q 



or p + 1 = q 



and 



which in a similar manner gives 



p + l = 3q\' 



* The other complicated forms, e. a., F !k+it-> -=-j 1+- ; ^ \ etc., 



, . . . .. ,' /' (2 2b 2n n \ 



are at once seen to be inapplicable here. 



