Bar monies of the Second Type. 7 



From (16) we obtain, on squaring, 



_ v » (4n + 3) 2 r l rp , , 12 , 



-i » (2m--2n-iy'{2m + 2n + 2fJ_y 2 " +l[fi)i d ** 



the limits not requiring delicate considerations. Thus 



=_?_2f 1 1 1 } 



4m + l o l(2m-2n-l) 2 (2m + 2n + 2) 2 )" 



. . . (20) 



This can be expressed in Gamma functions. For the special 

 case ??i = 0, the value is 



\1 2 2'^3 2 4 2 ■••/" 6 ' 

 For m = l, it becomes 



? /I 1 A A A A' A 1 



~5 l i+ 8 4U /J ~5\4 + 12r 

 In general, the value may be written as 



-((ra? + (2^W + --- admL )}' 



or 



+ l\ 2 Vl 2+ 3 2 " f •••) ((2m + l; 2 + (2m + 2) 24 " 'Vi 



4 m 

 Finally, 



f , PWO?*^ s£i { I + £ 10 ^ r ^l ^ ^ 



