Smaller fractions in displayed formulae?

Question

How do you make script-sized fractions in display mode?

In certain cases, I find that \frac-based fractions are too large for my tastes in displayed formulae. For example, I feel that the fractions here stand out way too much compared to the exponents:

I can hack a workaround by writing things like \frac{_1}{^{24}}, but that seems like too much trouble. The result, however, does look more like what I want:

Alternatively, I can force text styling by writing things like {\textstyle\frac{1}{24}}. This feels cleaner to me, but I'm not sure it looks as readable as the earlier hacked version because the fractions are tighter vertically (great for text mode but a bit much for display mode).

What would you do?

\documentclass{minimal}
\begin{document}

\[ \cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n}
= 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \cdots \]

\[ \cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n}
= 1 - \frac{_1}{^2}x^2 + \frac{_1}{^{24}}x^4 - \frac{_1}{^{720}}x^6 + \cdots \]

\[ \cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n}
= 1 - {\textstyle\frac{1}{2}}x^2 + {\textstyle\frac{1}{24}}x^4
- {\textstyle\frac{1}{720}}x^6 + \cdots \]

\end{document}

Answer 1

Use amsmath's \tfrac or \dfrac constructs to forcibly write a fraction in text or display style. In amsmath.sty, these macros are defined via \genfrac

\newcommand{\dfrac}{\genfrac{}{}{}0}
\newcommand{\tfrac}{\genfrac{}{}{}1}

with the token 0/1 setting the math style to \displaystyle/\textstyle (2 is for \scriptstyle; 3 is for \scriptscriptstyle, for what it's worth).

Here's a MWE:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align*}
\cos x &= \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n}
= 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \dotsb\\[2\baselineskip]
\cos x &= \sum_{n=0}^\infty \dfrac{(-1)^n}{(2n)!} x^{2n}
= 1 - \dfrac{1}{2}x^2 + \dfrac{1}{24}x^4 - \dfrac{1}{720}x^6 + \dotsb \\[2\baselineskip]
\cos x &= \sum_{n=0}^\infty \tfrac{(-1)^n}{(2n)!} x^{2n}
= 1 - \tfrac{1}{2}x^2 + \tfrac{1}{24}x^4 - \tfrac{1}{720}x^6 + \dotsb
\end{align*}
\end{document}​

Answer 2

For optimal readability of the source code, you can just use \textstyle once and get the same result:

\documentclass{article}

\begin{document}

\[ \cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n}
= \textstyle 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \cdots \]

\end{document}

If in another context don't want the \textstyle to propagate, you can put everything inside braces:

{\textstyle 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \cdots}

This being said, in your example, using display fractions would be more coherent as you already have one inside the sum giving the cosine. Generally, it's not a good idea to have display and text fractions so close to each other in the same equation.

Answer 3

A more general way is to use \scalebox from package graphicx and define your own macros.

\documentclass{minimal}
\usepackage{amsmath}
\usepackage{graphicx}
\setlength{\parskip}{\medskipamount}

\begin{document}

\def\hmath#1{\text{\scalebox{1.6}{$#1$}}}
\def\lmath#1{\text{\scalebox{1.4}{$#1$}}}
\def\mmath#1{\text{\scalebox{1.2}{$#1$}}}
\def\smath#1{\text{\scalebox{.8}{$#1$}}}

\def\hfrac#1#2{\hmath{\frac{#1}{#2}}}
\def\lfrac#1#2{\lmath{\frac{#1}{#2}}}
\def\mfrac#1#2{\mmath{\frac{#1}{#2}}}
\def\sfrac#1#2{\smath{\frac{#1}{#2}}}

\def\pow{^\mmath}

Sizes: Huge , Large , Medium , Normal , Small

Displayed fractions: $\displaystyle \hfrac{x^k}{k!} = \lfrac{x^k}{k!} = \mfrac{x^k}{k!} = \frac{x^k}{k!} = \sfrac{x^k}{k!}$

Inline fractions: $\hfrac{x^k}{k!} = \lfrac{x^k}{k!} = \mfrac{x^k}{k!} = \frac{x^k}{k!} = \sfrac{x^k}{k!}$

Displayed exponents (normal,small): $\displaystyle \frac{dy}{dx} e \pow {\frac{1}{2}\int f(x)\ dx} = \sfrac{dy}{dx} e ^ {\frac{1}{2}\int f(x)\ dx}$

Inline exponents (medium,normal): $\mfrac{dy}{dx} e \pow {\frac{1}{2}\int f(x)\ dx} = \frac{dy}{dx} e ^ {\frac{1}{2}\int f(x)\ dx}$

Displayed combinations (medium,normal): $\displaystyle \mfrac{e \pow {k\ln(x)}}{\sqrt{2\pi k}{(\mfrac{k}{e})} \pow k} = \frac{e^{k\ln(x)}}{\sqrt{2\pi k}{(\frac{k}{e})}^k}$

Inline combinations (medium,normal): $\mfrac{e \pow {k\ln(x)}}{\sqrt{2\pi k}{(\mfrac{k}{e})} \pow k} = \frac{e^{k\ln(x)}}{\sqrt{2\pi k}{(\frac{k}{e})}^k}$

Displayed series (normal): $\displaystyle \cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \cdots$

Displayed series (small): $\displaystyle \cos x = \smath{\sum_{n=0}^\infty} \sfrac{(-1)^n}{(2n)!} x^{2n} = 1 - \sfrac{1}{2}x^2 + \sfrac{1}{24}x^4 - \sfrac{1}{720}x^6 + \cdots$

Inline series (medium): $\cos x = \mmath\sum_{n=0}^\infty \mfrac{(-1)^n}{(2n)!} x^{2n} = 1 - \mfrac{1}{2}x^2 + \mfrac{1}{24}x^4 - \mfrac{1}{720}x^6 + \cdots$

Inline series (normal): $\cos x = \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + \cdots$

Convergent series: $\hmath{ 1 = \dfrac{1}{2} + \smath{ \dfrac{1}{4} + \smath{ \dfrac{1}{8} + \smath{ \dfrac{1}{16} + \smath{ \dfrac{1}{32} + \smath{ \dfrac{1}{64} + \smath{ \dfrac{1}{128} } } } } } } }$

\end{document}