Thus, δjk is a function of the correlation between zj and zk: ρj,k. We explore the relationship between δjk and ρj,k by calculating δjk numerically for the values of ρj,k from -0.99 to 0.99 with the step of 0.01. The results are shown in Fig. 1. Since the curve of Fig. 1 is a convex curve symmetric about the y-axis, we can approximate the relationship between δjk and ρj,k using a tenth-order polynomial: (2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \delta_{jk} \doteq c_{1}\rho_{j,k}^{2}+c_{2}\rho_{j,k}^{4}+c_{3}\rho_{j,k}^{6} +c_{4}\rho_{j,k}^{8}+c_{5}\rho_{j,k}^{10}. $$ \end{document}δjk≐c1ρj,k2+c2ρj,k4+c3ρj,k6+c4ρj,k8+c5ρj,k10.
