Aumentar el espacio entre numerador y denominador.

Question

He creado dos fracciones (vea el ejemplo a continuación), pero el denominador está demasiado cerca de la barra de división. ¿Puedo cambiar esto de alguna manera?

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    Combining two Gaussians with mean $\mu_1, \mu_2$ and variance $\sigma_1^2, \sigma_2^2$ yields a new Gaussian with mean $\mu = \frac{\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2}$ and variance $\sigma^2 = \frac{1}{\frac{1}{\sigma_1^2} + \frac{1}{\sigma_2^2}}$
\end{document}

Answer 1

Tienes dos opciones principales:

• Cambiar de \frac{...}{...}notación - a notación de fracciones en línea

• Cambie para mostrar matemáticas para componer las fórmulas para \muy \sigma^2.

\documentclass{article}
\usepackage{amsmath} % for "\text" macro
\begin{document}

\noindent
1. OP's original version:

Combining two Gaussians with mean $\mu_1, \mu_2$ and variance $\sigma_1^2, \sigma_2^2$ yields a new Gaussian with mean $\mu = \frac{\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2}$ and variance $\sigma^2 = \frac{1}{\frac{1}{\sigma_1^2} + \frac{1}{\sigma_2^2}}$.

\medskip\noindent
2. Partial switch to inline-math notation

Combining two Gaussians with mean $\mu_1, \mu_2$ and variance 
$\sigma_1^2, \sigma_2^2$ yields a new Gaussian with mean 
$\mu = \frac{\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2}$ 
and variance $\sigma^2 = \frac{1}{1/\sigma_1^2 + 1/\sigma_2^2}$.

\medskip\noindent
3. Full switch to inline math notation

Combining two Gaussians with means $\mu_1$ and $\mu_2$ and 
variances $\sigma_1^2$ and $\sigma_2^2$ yields a new Gaussian 
with mean $\mu = (\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2)/(\sigma_1^2 + 
\sigma_2^2)$ and variance $\sigma^2 = 1/(1/\sigma_1^2 + 1/\sigma_2^2)$.

\medskip\noindent
4. Switch to display math

Combining two Gaussians with means $\mu_1$ and $\mu_2$ and 
variances $\sigma_1^2$ and $\sigma_2^2$ yields a new Gaussian 
with mean $\mu$ and variance $\sigma^2$ given by
\[
\mu=\frac{\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2} 
\quad\text{and}\quad 
\sigma^2 = \frac{1}{1/\sigma_1^2 + 1/\sigma_2^2}\,.
\]

\end{document} 

Answer 2

Aquí, conservo la fracción en su formato nativo \textstyle, pero agrego un búfer (predeterminado) de 1 punto encima y debajo del numerador y denominador de cada fracción, que se puede cambiar con un argumento opcional. Yo lo llamo \qfrac[]{}{}. El MWE muestra el antes y el después.

\documentclass{article}
\usepackage{stackengine,scalerel}
\stackMath
\newcommand\qfrac[3][1pt]{\frac{%
  \ThisStyle{\addstackgap[#1]{\SavedStyle#2}}}{%
  \ThisStyle{\addstackgap[#1]{\SavedStyle#3}}%
}}
\usepackage{amsmath}

\begin{document}
    Combining two Gaussians with mean $\mu_1, \mu_2$ and variance $\sigma_1^2, 
  \sigma_2^2$ yields a new Gaussian with mean $\mu = \frac{\sigma_2^2 \mu_1 + 
  \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2}$ and variance $\sigma^2 = 
  \frac{1}{\frac{1}{\sigma_1^2} + \frac{1}{\sigma_2^2}}$

   Combining two Gaussians with mean $\mu_1, \mu_2$ and variance $\sigma_1^2, 
  \sigma_2^2$ yields a new Gaussian with mean $\mu = \qfrac{\sigma_2^2 \mu_1 + 
  \sigma_1^2 \mu_2}{\sigma_1^2 + \sigma_2^2}$ and variance $\sigma^2 = 
  \qfrac[.5pt]{1}{\qfrac{1}{\sigma_1^2} + \qfrac{1}{\sigma_2^2}}$
\end{document}

Answer 3

Alternativamente, use \raisebox :

\documentclass{article}
\usepackage{amsmath}
\begin{document}
   Combining two Gaussians with mean $\mu_1, \mu_2$ and variance $\sigma_1^2, \sigma_2^2$ yields a new Gaussian with mean $\mu = \frac{\raisebox{.2in}{$\sigma_2^2 \mu_1 + \sigma_1^2 \mu_2$}}{\raisebox{-.2in}{$\sigma_1^2 + \sigma_2^2$}}$ and variance $\sigma^2 = \frac{\raisebox{.2in}{$1$}}{\raisebox{-.2in}{$\frac{1}{\sigma_1^2} + \frac{1}{\sigma_2^2}$}}$
\end{document}