MULTIPLICATION OF ELLIPTIC FUNCTIONS. 225 



(2w+ l)(2m + 2)ß,,„+.,, , + (9u'-4m')B,„^ , 



+ 4 { {m — 1 ',n- — m- \ B,,,,,^ ., + (>r — "2 m + 1 )(;r — '2m + 2)ß2w-2. 2 = > 



geDeralJy, 



(169) {2m+ l)(2m + 2)ü.„,.,,,,r + [(4/ + l)yr-4w-]52„,,2, 



+ (;r-2m+l)(;i2-2w+2)£2,«-2,2r-2 = , 

 and, lastly, 



(2w+ lX27;i + 2}5o„,+2.2«+2 + {{^m+l)}r-4:m'}B,„^,^ 



+ (n--2m+l){n?-2m + '2)B,„,^._^._^_^ = , 



By means of the above equations, we find 



(170) 



Bq = 1, -Dg = oT' 



B, = |^[(/i2-4) + 2(;i^-l)^-2], 



ij^ = !!Î!^Ili)[(,j2_l6)(«2_36) + ]2(;i2-l)(7i2-lG)A2+ 



+ 4(w-- l)(l5?r- r)l)k' + 32(11'- l)(;r- 9)A«] , 



2^^^^ = _ ^^^^j^ [.;r-lG)(u2-36)(/r-(34) + 2ü(;r-l):«--l6;(«2-86U-2 



+ 12(71^- l)(;r-9X29/r- 104)Ä;* 

 + 64(7v^ - 1 )(?J- - 9)(7 7i2 _ 22)/.« 

 + r28(/r- l)(/i2_ y)(H2_ 16)A«], 



