Cornish-Fisher expansion of w

We apply cfexpw to cumulantw.

[Graphics:../Images/index_gr_1060.gif]
[Graphics:../Images/index_gr_1061.gif]
[Graphics:../Images/index_gr_1062.gif]
[Graphics:../Images/index_gr_1063.gif]
[Graphics:../Images/index_gr_1064.gif]
[Graphics:../Images/index_gr_1065.gif]
[Graphics:../Images/index_gr_1066.gif]

The following zformula is defined as [Graphics:../Images/index_gr_1067.gif].

[Graphics:../Images/index_gr_1068.gif]
[Graphics:../Images/index_gr_1069.gif]
[Graphics:../Images/index_gr_1070.gif]
-v0 + w + o*(-cr[0] - td[al1, au1] + 
   w^2*(-cr[2] + tp3[9, 9, 9]/6) - tp3[9, 9, 9]/6 -
   (v0^2*tp3[9, 9, 9])/3 + (v0*w*tp3[9, 9, 9])/6) +
o^2*(v0^3*(tp3[9, 9, 9]^2/18 + (tp3[9, 9, al1]*tp3[9, 9, au1])/8 -
     tp4[9, 9, 9, 9]/8) + v0*(td[al1, au2]*td[al2, au1] -
     (cr[0]*tp3[9, 9, 9])/6 - (td[al1, au1]*tp3[9, 9, 9])/6 +
     (5*tp3[9, 9, 9]^2)/72 + (tp3[9, 9, al1]*tp3[9, 9, au1])/8 -
     tp4[9, 9, 9, 9]/24) + v0*w^2*(-(cr[2]*tp3[9, 9, 9])/6 -
     tp3[9, 9, 9]^2/24 + tp4[9, 9, 9, 9]/24) +
   w^3*(-cr[3] - (cr[2]*tp3[9, 9, 9])/3 - tp3[9, 9, 9]^2/72 +
     tp4[9, 9, 9, 9]/24) + w*(-cr[1] + td[al1, au2]*td[al2, au1] -
     (cr[0]*tp3[9, 9, 9])/3 + (td[al1, au1]*tp3[9, 9, 9])/6 +
     (13*tp3[9, 9, 9]^2)/72 + (tp3[9, 9, al1]*tp3[9, 9, au1])/2 -
     td[au1, au2]*tp3[9, al1, al2] +
     (tp3[9, al1, au2]*tp3[9, al2, au1])/2 +
     v0^2*(-(tp3[9, 9, al1]*tp3[9, 9, au1])/8 +
       tp4[9, 9, 9, 9]/24) - tp4[9, 9, 9, 9]/8 -
     tp4[9, 9, al1, au1]/4))

Get the coefficients of [Graphics:../Images/index_gr_1071.gif] for zformula.

[Graphics:../Images/index_gr_1072.gif]
[Graphics:../Images/index_gr_1073.gif]
[Graphics:../Images/index_gr_1074.gif]

[Graphics:../Images/index_gr_1075.gif]

[Graphics:../Images/index_gr_1076.gif]
[Graphics:../Images/index_gr_1077.gif]

[Graphics:../Images/index_gr_1078.gif]

[Graphics:../Images/index_gr_1079.gif]
[Graphics:../Images/index_gr_1080.gif]

[Graphics:../Images/index_gr_1081.gif]

[Graphics:../Images/index_gr_1082.gif]
[Graphics:../Images/index_gr_1083.gif]

[Graphics:../Images/index_gr_1084.gif]

[Graphics:../Images/index_gr_1085.gif]
[Graphics:../Images/index_gr_1086.gif]

[Graphics:../Images/index_gr_1087.gif]

[Graphics:../Images/index_gr_1088.gif]
[Graphics:../Images/index_gr_1089.gif]

[Graphics:../Images/index_gr_1090.gif]

[Graphics:../Images/index_gr_1091.gif]
[Graphics:../Images/index_gr_1092.gif]

[Graphics:../Images/index_gr_1093.gif]

[Graphics:../Images/index_gr_1094.gif]
[Graphics:../Images/index_gr_1095.gif]

[Graphics:../Images/index_gr_1096.gif]

[Graphics:../Images/index_gr_1097.gif]
[Graphics:../Images/index_gr_1098.gif]

[Graphics:../Images/index_gr_1099.gif]

[Graphics:../Images/index_gr_1100.gif]
[Graphics:../Images/index_gr_1101.gif]

[Graphics:../Images/index_gr_1102.gif]

[Graphics:../Images/index_gr_1103.gif]
[Graphics:../Images/index_gr_1104.gif]

[Graphics:../Images/index_gr_1105.gif]

[Graphics:../Images/index_gr_1106.gif]
[Graphics:../Images/index_gr_1107.gif]

[Graphics:../Images/index_gr_1108.gif]

[Graphics:../Images/index_gr_1109.gif]
[Graphics:../Images/index_gr_1110.gif]

[Graphics:../Images/index_gr_1111.gif]

[Graphics:../Images/index_gr_1112.gif]
[Graphics:../Images/index_gr_1113.gif]

[Graphics:../Images/index_gr_1114.gif]

[Graphics:../Images/index_gr_1115.gif]
[Graphics:../Images/index_gr_1116.gif]

[Graphics:../Images/index_gr_1117.gif]

[Graphics:../Images/index_gr_1118.gif]
[Graphics:../Images/index_gr_1119.gif]

[Graphics:../Images/index_gr_1120.gif]

[Graphics:../Images/index_gr_1121.gif]
[Graphics:../Images/index_gr_1122.gif]


Converted by Mathematica      July 21, 2003