WH 
m 
AI(w)n = u-A 1 -^ r + A 2 -r-, H (— 1 ) n A„ 
18 ÜBER DIE ENTWICKLUNG DER MODULAR - FUNCTIONEN. 
t 2» + l 
3’ ‘ " 2 5’ ■ v ' " (2n+ly + ‘‘ 
Aj = 1 + ¥ 
A 2 = 1 + 7b 4 + 47b 2 
A 3 = 1 + 7c 8 + 9 (7c 2 + ¥) 
A t = 1 + ft 8 + 16 (7c 2 + 7c 8 ) — 67c 4 
Ä 5 = 1 + 7c 10 + 25 (Ä 2 + 7c 8 )- 494 (¥ + 7c 8 ) 
= l + fc 12 +36(7c 2 + 7c 10 )-5781 (T; 4 + 7; 8 )- 121847c 8 
= l + 7c 14 +49(7c 2 + 7c 12 )-55173(7c 4 + 7c ,0 )-179605(£ 8 + Ä; 8 ) 
= ! + ä 18 + 64 (7c 2 + 7c 14 ) - 502892 (7c 4 + 7c 12 ) - 2279488 (¿ 8 + 1c 10 ) - 3547930 ¥ 
= l + 7c 18 + 81 (& 2 +& 18 ) - 4537500 (7c 4 + 7c 14 ) - 27198588 (7c 8 +£ 12 ) - 59331498 (£ 8 + 1c 10 ) 
A* l0 = 1 + 7c 20 + 100(7c 2 + 7c 18 ) - 40856715 (7c 4 + 7c 18 ) - 313180080(¥ + 7c 14 ) - 909015270 (7c 8 +& 12 ) 
-1278530856 £ 10 
u. s. w. 
0/2 0/^ 4/2» 
AI(m), = ! —-Bi _ 2 r + ^2^7 + + ”* 
Bj = 1 
-B 2 = 1 + 27c 2 
_B 3 = 1 + 6/b 2 + 87c 4 
= l + 127c 2 + 607c 4 + 327c 6 
jß. = 1 + 20 7c 2 + 348 ¿ 4 + 448 7c 6 + 128 ¿ 8 
JB e = 1 + 30 7c 2 + 237 2 7c 4 + 4600 7c 8 + 2880 ¿ 8 +512 7c 10 
_B 7 = 1 + 42 ¿ 2 + 19308 7c 4 +51816 7c 8 +45024 ¿ 8 + 16896 7c 10 + 2048 7L J2 
J5 8 = 1 + 56 7c 2 + 169320 & 4 + 6280647;®+ 757264 7c 8 + 370944 7t 10 + 931847; I2 + 8192 7; 14 
JB 9 = 1 + 7 2 7c 2 + 1515368 7c 4 + 7594592 7c 8 + 12998928 7c 8 + 9100288 7c 10 + 27258887c 12 
+ 491520 ¥*+ 32768 7; 18 
JB 10 = 1 + 90 7c 2 + 13623480 £ 4 + 893480807c 8 + 211064400 7c 8 + 2193618247c ,0 + 1002429447; 12 
+ 18450432 ft 14 + 2506752 7; 18 + 131072& 18 
u. s. w. 
Al(w) 3 
1 TV ^ , 73' ^ 
^ -^1 2’ "^ 2 4’ 
+ (-i)-b; 
(2n) 
r + 
7c 2 
27; 2 + fc 4 
87c 2 + 67c 4 + 7c 8 
32 F+ 60 7c 4 + 12 7c 8 +7c 8 
128 7c 2 + 448 ¥ + 348 7c 8 + 20 7c 8 + 7c 10 
5127c 2 + 2880 7c 4 + 46007c 8 + 2372£ 8 + 307c 10 + 7; 12 
2048 7c 2 + 16896 7c 4 +45024 7c 6 + 51816 7c 8 + 19308 7c 10 + 42 £ 12 + 7c 14 
8192 7c 2 + 93184 7c 4 + 370944 7c 6 + 7572647c 8 +6280647c 10 + 169320 7c 12 + 56 7c 14 +7c 18 
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