$\exp x = 1 + x + x^2/2 + x^3/6 + x^4/24 + \cdots$.
$\exp x = 1 + x + x^2/2 + x^3/6 + x^4/24 + \cdots$.
\begin{align*} & \Z\subset\Q\subset\R\subset\C \\ & \diag(a_1,\ldots,a_n) = \begin{bmatrix} a_1 & 0 & \cdots & 0 \\ 0 & a_2 & \ddots & \vdots \\ \vdots & \ddots & \ddots & 0 \\ 0 & \cdots & 0 & a_n \\ \end{bmatrix} \qquad (\text{diagonal matrix}) \\ & a\mapsto\np{:}{a} \qquad \text{(the normal ordering of $a$)} \end{align*}
Here \Z
, \Q
, \R
, \C
, \diag
, and \np
are defined in MyConfig.js.
\begin{align*} & \Z\subset\Q\subset\R\subset\C \\ & \diag(a_1,\ldots,a_n) = \begin{bmatrix} a_1 & 0 & \cdots & 0 \\ 0 & a_2 & \ddots & \vdots \\ \vdots & \ddots & \ddots & 0 \\ 0 & \cdots & 0 & a_n \\ \end{bmatrix} \qquad (\text{diagonal matrix}) \\ & a\mapsto\np{:}{a} \qquad \text{(the normal ordering of $a$)} \end{align*}