通用公式:A(x)=1+x-7*x^3+242*x^5-17771*x^7+2189294*x^9-+。。。
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设F(x)=A(x/F(x)^2),使得A(x)=F(x*A(x)^2),则
F(x)=1+x-2*x^2+26*x^4-1378*x^6+141202*x^8-+。。。
[1,1,-2,0,26,0,-1378,0,141202,0,-22716418,0,5218302090,0,...].
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G.F.A(x)奇数负幂系数。
A^1:[(1),1,0,-7,0242,0,-17771,02189294,0,-404590470,0,…];
A^-1:[1,(-1),1,6,-13,-22250616932,-37709,-21271264595294,…];
A^-3:[1,-3,(6),11,-69,-537280645282,-215781,-5963673,…];
A^-5:[1,-5,15,(0),-140,-601624562380,-503935,-8911515,…];
A^-7:[1,-7,28,-35,(-182),-392996865519,-860825,-10670499,…];
A^-9:[1,-9,45,-102,-135,(0),1312854504,-1240416,-11070241,…];
A^-11:[1,-11,66,-209,77341,(15158),31460,-1598696,-10074240,…];
A^-13:[1,-13,91,-36454622116107,(0),-1899508,-7767240,…];
A^-15:[1,-15120,-5751380,-97817040,-36375,(-2118030),…];
A^-17:[1,-17153,-8502703,-411420502,-76772,-2240175,(0),…];
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缩放后,括号中显示的系数
构成函数F(x)=A(x/F(x)^2)的系数:
F: [1、-1/(-1)、6/(-3)、0、-182/(-7)、015158/(-11)、0,-2118030/(-15),0,…]。
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