218 K- FUJISAWA. 



D,^, = ( - 1) V ''('''- ^ ) k'^^^{{n'- 9)(1 4- k') + 2{2u'- 3)¥ \ , 



D^-, = -(-l)V ^K^^^^ ^^ F^-\l + F) , 



D,p = (-1)"2 7^ A;2^. 



The first five coefficients were given by Jacobi himself. Tlie first 

 and the last six coefficients of all the four functions have been found 

 by Baehr by a different method. 



§ 17. 



Let us now consider the rational integral functions of .t'\ B, C 

 which enter into the numerators of en nn and dn nit, n beino- odd. 

 From the well-known relations 



(151) B{x,k) = c(J^,k^};^^x\ C{x,k) = B{j^,l>jk 



(152) B (kx, -^ = G {X, k), C (kx, -j) = B {x, k), 

 we deduce 



(153) B (kx, j) = B (-^ , k\ k'" x'", 



2?) rpip 



whence 



(154) B,,_,„,{k) = B,^ (j^ ¥^, B,Jk) = i?,,-.2.(y) F^ 



