Cornish-Fisher Asymptotic Expansion

$\displaystyle w$	$\textstyle =$	$\displaystyle x+[\gamma_1h_1(x)]+[\gamma_2 h_2(x)+{\gamma_1}^2 h_{11}(x)]$
	$\textstyle \phantom{=}$	$\displaystyle +[\gamma_3h_3(x)+\gamma_1\gamma_2h_{12}(x)+{\gamma_1}^3h_{111}(x)]$
	$\textstyle \phantom{=}$	$\displaystyle +[\gamma_4h_4(x)+{\gamma_2}^2 h_{22}(x)+\gamma_1\gamma_3 h_{13}(x)$
	$\textstyle \phantom{=}$	$\displaystyle +{\gamma_1}^2\gamma_2 h_{112}(x)+{\gamma_1}^4h_{1111}(x)]+\ldots,$

$\displaystyle h_1(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 6}} \mathop{\rm He}\nolimits_2(x)$
$\displaystyle h_2(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 24}} \mathop{\rm He}\nolimits_3(x)$
$\displaystyle h_{11}(x)$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 36}} [2\mathop{\rm He}\nolimits_3(x)+\mathop{\rm He}\nolimits_1(x)]$
$\displaystyle h_{3}(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 120}} \mathop{\rm He}\nolimits_4(x)$
$\displaystyle h_{12}(x)$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 24}} [\mathop{\rm He}\nolimits_4(x)+\mathop{\rm He}\nolimits_2(x)]$
$\displaystyle h_{111}(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 324}} [12\mathop{\rm He}\nolimits_4(x)+19\mathop{\rm He}\nolimits_2(x)]$
$\displaystyle h_4(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 720}}\mathop{\rm He}\nolimits_5(x)$
$\displaystyle h_{22}(x)$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 384}} [3\mathop{\rm He}\nolimits_5(x)+6\mathop{\rm He}\nolimits_3(x)+2\mathop{\rm He}\nolimits_1(x)]$
$\displaystyle h_{13}(x)$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 180}}[2\mathop{\rm He}\nolimits_5+3\mathop{\rm He}\nolimits_3(x)]$
$\displaystyle h_{112}(x)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 288}}[14\mathop{\rm He}\nolimits_5(x)+37\mathop{\rm He}\nolimits_3(x)+8\mathop{\rm He}\nolimits_1(x)]$
$\displaystyle h_{1111}(x)$	$\textstyle =$	$\displaystyle -{\textstyle{1\over 7776}} [252\mathop{\rm He}\nolimits_5(x)+832\mathop{\rm He}\nolimits_3(x)+227\mathop{\rm He}\nolimits_1(x)].$