388 



where (^ is given by Eq, (29). 



The function h^ ' {x,'Y) has the following properties: 



(35: 



^ Ci*-x*r (36) 



The properties of h^"^'^^ as well as h^-^^^^ and h^^ for large ;^ will 

 not be considered here because they have little physical significance 



in this range for reasons to be stated near the end of this section. 



(1/2) (3/2) (5/2) 

 This limitation applies also to y , y , and y ; however, the 



behavior of these functions is considered for large ^ because of its 



intrinsic interest. 



The functions y^ ' (xj-jr*) and h ' (x, 1^) are presented 

 in Tables I and II, respectively. 



The maxiinum value of h^-^^^^ (x, f ) occurs at x = and ^ = 

 ^ 11/21 = 1.10 and has a value h^^S) = h^VS) (0,^1^^^^) = 0.07222. 



Case (2). l/= 3/2 



The solution for this case is 



^^'/-)Cx,t)= -f^y (37) 



where ^ is given by Eq. (29). Some properties of y ' {x.,Tf) are: 



-y'"-'C^-'-7;^.A. ^«li (3,) 



71 



