Table 1: Expression of four components of the shear three-point function where ${C_{\alpha}(l_3)}=-l_3^{-4 - 3~\alpha} {\pi }^3~{\csc (\frac{\alpha~\pi }{2} )... ... ) / ({2~\Gamma{ (2 -\frac{3~\alpha}{2} )}~{\Gamma ({\frac{\alpha}{2}}} )^3} )$ .

$\displaystyle \xi_{\gamma(\vec{r}_1)\gamma(\vec{r}_2)\gamma(\vec{r}_3)}$	=	$\displaystyle -\frac{{C_{\alpha}(l_3)}~{\alpha}^2~{\left( 2 + \alpha \right) }^... ...+ z_3^2 \right) + 8~\left( 1 - 2~z_3 + 4~z_3^3 - 2~z_3^4 \right) \right.\right.$
		$\displaystyle \left.\left.+ 3~{\alpha}^2~ \left( -4 + 5~z_3 + 3~z_3^2 - 16~z_3^... ...c{3~\alpha}{2}\right)~\Muserfunction{R1}(0,z)~ \Muserfunction{R1b}(0,z) \right.$
		$\displaystyle \left. + 8~\left( 1 + \alpha \right) ~\left( 2 - 5~z_3 + 2~z_3^2 ... ...c{3~\alpha}{2}\right)~ \Muserfunction{R1}(1,z)~\Muserfunction{R1b}(0,z) \right.$
		$\displaystyle \left. - {\ifthenelse{\equal{Gamma}{Gamma}}{\Gamma}{Gamma}}\left(... ... \right) + 8~\left( 1 - 2~z_3 + 4~z_3^3 - 2~z_3^4 \right) \right.\right.\right.$
		$\displaystyle \left.\left.\left. + 3~{\alpha}^2~\left( -4 + 5~z_3 + 3~z_3^2 - 16~z_3^3 + 8~z_3^4 \right) \right) ~\Muserfunction{R2}(0,z) \right.\right.$
		$\displaystyle \left.\left. +8~\left( 1 + \alpha \right) ~\left( 2 - 5~z_3 + 2~z... ...^5 \right) ~\Muserfunction{R2}(1,z) \right] ~ \Muserfunction{R2b}(0,z) \right\}$	(24)
$\displaystyle \xi_{\gamma(\vec{r}_1)\gamma(\vec{r}_2)\overline{\gamma}(\vec{r}_3)}$	=	$\displaystyle - \frac{{C_{\alpha}(l_3)}~{\alpha}^2~\left( 2 + \alpha \right)}{\... ...ft( 8~\left( -1 + z_3 \right) ~z_3\phantom{-1 - 8~z_3 + 8~z_3^2} \right.\right.$
		$\displaystyle \left.\left.\left.\left. + \alpha~\left( -1 - 8~z_3 + 8~z_3^2 \ri... ...z_3 \right) ~\left( 2~\left( -1 + z_3 \right) ~z_3 \right.\right.\right.\right.$
		$\displaystyle \left.\left.\left.~+ \alpha~\left( -1 - 2~z_3 + 2~z_3^2 \right) \... ...b}}{\overline{z}_3}{}} \right) ~\Muserfunction{R1b}(1,z) \right) \bigg] \right.$
		$\displaystyle \left. + {\ifthenelse{\equal{Gamma}{Gamma}}{\Gamma}{Gamma}} \left... ...t( -1 - 8~z_3 + 8~z_3^2 \right) \right) ~\Muserfunction{R2}(0,z) \right.\right.$
		$\displaystyle \left.\left. + 4~\left( -1 + 2~z_3 \right) ~\left( 2~\left( -1 + ... ...] ~\left( \left( -2 + 3~\alpha \right) ~\Muserfunction{R2b}(0,z) \right.\right.$
		$\displaystyle \left.+ 4~\left( -1 + 2~{\ifthenelse{\equal{zb}{zb}}{\overline{z}_3}{}} \right) ~\Muserfunction{R2b}(1,z) \right) \bigg\}$	(25)
$\displaystyle \xi_{\gamma(\vec{r}_1)\overline{\gamma}(\vec{r}_2){\gamma}(\vec{r}_3)}$	=	$\displaystyle \frac{{C_{\alpha}(l_3)}~\alpha~\left( 2 + \alpha \right)}{{\left(... ..._3}}{\Gamma}{z_3}} + \alpha~\left( -1 - 5~z_3 + 2~z_3^2 \right) \right) \right.$
		$\displaystyle \left.\left. \times\Muserfunction{R1}(0,z) +4~\left( 1 + z_3 \rig... ...t( 1 - 4~z_3 + z_3^2 \right) \right) ~ \Muserfunction{R1}(1,z) \right]~ \right.$
		$\displaystyle \left.\times \left[ \left( -2 + 3~\alpha \right) ~\left( 1 + 2~{\... ...b}{zb}}{\overline{z}_3}{}}}^2 \right) ~\Muserfunction{R1b}(1,z) \right] \right.$
		$\displaystyle \left.+ \alpha~{\ifthenelse{\equal{Gamma}{Gamma}}{\Gamma}{Gamma}}... ...( -1 - 5~z_3 + 2~z_3^2 \right) \right) ~ \Muserfunction{R2}(0,z) \right.\right.$
		$\displaystyle \left.\left.+ 4~\left( 1 + z_3 \right) ~\left( -2~z_3 + \alpha~\left( 1 - 4~z_3 + z_3^2 \right) \right) ~ \Muserfunction{R2}(1,z) \right] ~ \right.$
		$\displaystyle \times \left[ \left( -2 + 3~\alpha \right) ~\left( 1 + 2~{\ifthen... ...b}{zb}}{\overline{z}_3}{}}}^2 \right) ~\Muserfunction{R2b}(1,z) \right] \bigg\}$	(26)
$\displaystyle \xi_{\gamma(\vec{r}_1)\overline{\gamma}(\vec{r}_2)\overline{\gamma}(\vec{r}_3)}$	=	$\displaystyle \frac{{C_{\alpha}(l_3)}~\alpha~\left( 2 + \alpha \right)}{\left( ... ...alpha~\left( 9 - 6~z_3 \right) + 4~z_3 \right) ~\Muserfunction{R1}(0,z) \right.$
		$\displaystyle \left.\left. - 4~\left( -2 + z_3 \right) ~z_3~\Muserfunction{R1}(... ...{\overline{z}_3}{}}}^2 \right) \right) ~\Muserfunction{R1b}(0,z) \right.\right.$
		$\displaystyle \left.\left.+ 4~\left( -2 + {\ifthenelse{\equal{zb}{zb}}{\overlin... ...equal{Gamma}{Gamma}}{\Gamma}{Gamma}} \left(1 - \frac{\alpha}{2}\right)~ \right.$
		$\displaystyle \left. \times \left[ \left( -2 + 3~\alpha \right) ~\left( -3 + 2~... ...}(0,z) + 4~\left( -2 + z_3 \right) ~z_3~\Muserfunction{R2}(1,z) \right] \right.$
		$\displaystyle \left.\times \left[ \left( -2 + 3~\alpha \right) ~\left( 4~\left(... ...{\overline{z}_3}{}}}^2 \right) \right) ~\Muserfunction{R2b}(0,z) \right.\right.$
		$\displaystyle \left.+ 4~\left( -2 + {\ifthenelse{\equal{zb}{zb}}{\overline{z}_3... ...\overline{z}_3}{}}}^2 \right) \right) ~\Muserfunction{R2b}(1,z) \right] \bigg\}$	(27)

Source LaTeX | All tables | In the text

	1 Introduction
	2 A complex variable representation
	3 Correlation functions in the one-halo model
	4 Shear patterns in the one-halo model
	5 Prospects
	References