\(\newcommand{\D}{\text{d}} \newcommand{\I}{\text{i}} \newcommand{\E}{\text{e}} \newcommand{\Prob}{\mathbb{P}} \newcommand{\Expect}{\mathbb{E}} \newcommand{\Var}{\text{Var}} \newcommand{\PAvg}[1]{\left[#1\right]} \newcommand{\Avg}[1]{\left\langle#1\right\rangle} \newcommand{\AvgJ}[1]{\Avg{#1}_{\bm J}} \newcommand{\AvgDyn}[1]{\Avg{#1}_{\text{dyn.}}} \newcommand{\CAvg}[2]{\Avg{#1}_{\left|#2\right.}} \newcommand{\Devi}{\mathfrak{d}}\)
計算テクニック
和の積の計算のための添字テクニック
\[ \left(
\sum_i a_i
\right)
\left(
\sum_i b_i
\right)
=
\left(
\sum_i a_i
\right)
\left(
\sum_j b_j
\right)
=
\sum_i \sum_j a_i b_j\]
\[ \left(
\sum_i a_i
\right)^2
=
\sum_i \sum_j a_i a_j\]