THIRD ELLIPTIC INTEGRAL AND THE ELLTPSOTOMIC PROBLEM. 



49. p = 32, V - K +/K't, /= ! 3. 5. 7,9.^11.13. 15 



and this leads to 



3 - (1 + 2m 



" (a - m)* 



2m 2 ) /8 2 + 4 (m - m 2 ) - (m - m") 



- /3 (ft - 1) (/3 - 1 + 2m - 2m 2 ) a = 



so that 



2 2 (1 + n) 2/3 (2 + ) + 1 



6(1 + &) 

 (1 + 6)(1 + 2b - U 2 + 26) 



= 



a C 6 in (a, b). 

 Put b = ac, 



a quadratic in a 2 , 



{(1 + 26) 2 - a 4 

 |3 a (a* + 1)' 



*c (c 4 + 2c :3 + + -- 1) -' + c = 



c 4 + 2(-'' + + 01 



a 



( - 'T = 



a = X/C ' 3 + l C * + 2c - 1 + (r + 1 



6 = 



. C 2 + 2c - 1 + (c + L) y/c 2 - 



(c+l)(c-l)r(c 8 +l)(c* + 2c-l) 



4c 



(c 2 - I) 4 

 4c 4 



-] 



301 

 (1). 



(2), 



(3), 



(4), 

 (5), 



(6), 



(7), 

 (8), 

 (9). 



(11), 



(12), 

 (13), 



