  In my previous paper about SRWS-$\zeta$ theory[Y.Ueoka,viXra:2205.014,2022],
I proposed an approximation of rough averaged summation of typical critical
Green function for the Anderson transition in the Orthogonal class. In this
paper, I remove a rough approximate summation for the series of the typical
critical Green function by replacing summation with integral. Pade approximant
is used to take a summation. The perturbation series of the critical exponent
$\nu$ of localization length from upper critical dimension is obtained. The
dimensional dependence of the critical exponent is again directly related with
Riemann $\zeta$ function. Degree of freedom about lower critical exponent
improve estimate compared with previous studies. When I fix lower critical
dimension equal to two, I obtained similar estimate of the critical exponent
compared with fitting curve estimate of the critical exponent[E.Tarquini et
al.,PhysRevB.95(2017)094204]. 1
