MULTIPLICATION OF ELLIPTIC FUNCTIONS. 217 



and, lastly, 



{Im + 2)(27?i + 3)D4;^2,n-2, 2p-m-2 + (2WI + l)(n2— 2wi - 1)-Di„_2m, 2?>-m 

 + {(2m+ 5)7^2- (2?;i+ l)n ^.p-2,«, 2p-,H-2 



+ («2— 2w)(7?2-2?» + l)D4„_2m+2,2;.-«, == , 



or 



{%n + 2)(2wi + 3)D,,_2„^2, 2;.-«-i + 2 1 (27;^. + ^)n^ - ßm +}y-} D,^,^^ ,,^^_, 



+ (?i2— 2??i)(7l2— 27?i+l)D4p_2,„+2,2j^^ + l = , 



according as m is even or odd. 



From the above equations, we find 



(150) 



A^i2 = (-1) ' 13 ; ^ ^ Ä;^^^^M(^^— 25)(».^-49)(;^^-81)(7?.^-121)(1 + A:^^) 



+ 6(n2_25)(H2_49)(7?.2-81)(6?r-ll)(A=^+P') 



- 3(l927';i«- 330687^''- 962«* 



+ 1033308»2_ 1819125XÄ'' + A*^) 



- 4(3046??« - 38037;/« + 327997?.* 



+ 7086477^2- 1299375)Ä«} , 



■^4p— 10 



_(_1) 2 /^^^^ ^'11^ — J_A"2p-io|(,^2_25)(,;2_49)(^j2_8i)(i^7,io) 



+ 5(7i2_25X?i2-49)(57?2-9)(A-+ A'«) 

 - 2(24771«+ 325?i*- 137577?H 23625)(A'' + /-") } , 



A^8 = (-1) ' ^ ,j ; ^ F^-M(»— ^)(v^^-25X^^^-49)(l + A'«) 



+ 4(7i2- 9X7i2_ 25X47?2- 7)(F + A") 



-6(7i''+857i*-67l7i2+945)Ä*}, 



