math.tex (1338B)
1 \usepackage{amsmath} 2 \usepackage{amssymb} 3 \usepackage{amsthm} 4 5 % custom mathematical expressions 6 \newcommand{\Var}[1]{\sigma_{#1}^2} 7 \newcommand{\Fourier}[1]{\mathcal{F}\left\{#1\right\}} 8 \newcommand{\InverseFourier}[1]{\mathcal{F}^{-1}\left\{#1\right\}} 9 \newcommand{\Fun}[1]{\mathcal{D}_1\left(x,#1\right)} 10 \newcommand{\FunSecond}[1]{\mathcal{D}_2\left(x,#1\right)} 11 \newcommand{\FunThird}[1]{\mathcal{D}_2\left(x,#1\right)} 12 \newcommand{\FunThreeD}[1]{\mathcal{D}_3\left(x,y,#1\right)} 13 \newcommand{\Sinh}[1]{\cosh\left(#1\right)} 14 \newcommand{\SinhX}[1]{\sinh\left(#1\right)} 15 16 \newcommand{\FourierY}[2]{\mathcal{F}_{#2}\!\left\{#1\right\}} 17 \newcommand{\InverseFourierY}[2]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}} 18 19 \newcommand{\FourierX}[3]{\mathcal{F}_{#2}\!\left\{#1\right\}\!\left(#3\right)} 20 \newcommand{\InverseFourierX}[3]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}\!\left(#3\right)} 21 22 % properly aligned version of sqrt for \zeta_y^2 23 \newcommand{\SqrtZeta}[1]{\sqrt{\vphantom{\zeta_x^2}\smash[b]{#1}}} 24 25 % normalisation 26 \newcommand{\SqrtZetaX}{\sqrt{1 + \zeta_x^2}} 27 \newcommand{\SqrtZetaY}{\SqrtZeta{1 + \zeta_x^2 + \zeta_y^2}} 28 \newcommand{\FracSqrtZetaX}[1]{\frac{#1}{\SqrtZetaX{}}} 29 \newcommand{\FracSqrtZetaY}[1]{\frac{#1}{\SqrtZetaY{}}} 30 31 % wave vector 32 \newcommand{\Kvec}{\vec{k}} 33 \newcommand{\Kveclen}{\lvert\smash[b]{\Kvec}\rvert} 34