Need some help with perfecting the layout

\documentclass{article}
\usepackage{amsmath}
\setlength{\parindent}{0pt}
\newcommand{\fac}{n!}
\newcommand\test[3]{\left(\begin{array}{@{\,}c@{\,}} #1 \\ #2 \end{array}\middle|\ \ #3 \right)}
\begin{document}

Dit gedeelte is gewijd aan de wiskundige berekening van de inproducten tussen de vectoren $u_0(E), u_1(E), v(x)$ en $w(p)$. Twee bestaande formules zullen hierbij van cruciaal belang blijken te zijn.\\

De eerste formule zegt dat

\begin{align*}
\sum_{n=0}^{\infty} \frac{(a)_n}{\fac}F_1 \test{-n,b}{a}{y}_1 F_1& \test{-n}{a}{x} t^n\\
&=(1-t)^{b-a}(1-t+yt)^{-b} e^{\frac{xt}{t-1}}F_1 \test{b}{a}{\frac{xyt}{(1-t)(1-t+yt)}},\\
\end{align*}
waarbij $|t| <1.$\\

De tweede formule is de volgende benadering:

\begin{equation*}
\lim_{z \rightarrow \infty} F_1 \test{c}{a}{z} = \lim_{z \rightarrow \infty} \frac{\Gamma(a)}{\Gamma(c)} e^z z^{c-a} \sum_{n=0}^{\infty} \frac{(a-c)_n (1-c)_n}{\fac} z^{-n}
\end{equation*}
\end{document}


Looking at the arrows you can see that the spacing is different. On the second picture the spacing between the letters seems bigger, the spacing between the two lines is also bigger

In the equation I didn't manage to get the alignment right. I'm assuming that one line is flushedleft and the other centered. The fraction in the first image is much smaller than in the 2nd one.

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tip: If you indent lines by 4 spaces or enclose words in backticks , they'll be marked as code, as can be seen in my edit. You can also highlight the code and click the "code" button (with "{}" on it). – hpesoj626 Dec 12 '12 at 16:33
Does this post answer your question? tex.stackexchange.com/questions/47400/… – hpesoj626 Dec 12 '12 at 16:38
I don't quite understand... Are you trying to replicate the layout of the first image? How did you produce the first image? – JLDiaz Dec 12 '12 at 16:51
Yes, I'm trying replicate the first image. The first image was not made by me in tex, but copied from a pdf. – min Dec 12 '12 at 16:55
the fraction in the first display probably uses \tfrac (it's text rather than display style, but i'm not convinced that's a great choice). egreg has already pointed out that multline is what you want, not align. – barbara beeton Dec 12 '12 at 20:32

The first example is probably typeset like this, although I have made some slight changes that I will illustrate later.

\documentclass{article}
\usepackage[dutch]{babel}
\usepackage{amsmath}

%\setlength{\parindent}{0pt}
%\setlength{\parskip}{\medskipamount}

\newcommand{\fac}{n!}
\newcommand\test[3]{%
\left(\begin{array}{@{\,}c@{\,}}
#1 \\ #2 \end{array}\middle|\;#3 \right)}

\begin{document}

Dit gedeelte is gewijd aan de wiskundige berekening van de inproducten
tussen de vectoren $u_0(E)$, $u_1(E)$, $v(x)$~en~$w(p)$. Twee bestaande
formules zullen hierbij van cruciaal belang blijken te zijn.

De eerste formule zegt dat
\begin{multline*}
\sum_{n=0}^{\infty} \frac{(a)_n}{\fac}F_1 \test{-n,b}{a}{y}_1 F_1 \test{-n}{a}{x} t^n\\
=(1-t)^{b-a}(1-t+yt)^{-b} e^{\frac{xt}{t-1}}F_1 \test{b}{a}{\frac{xyt}{(1-t)(1-t+yt)}},
\end{multline*}
waarbij $|t| <1$.

De tweede formule is de volgende benadering:
\begin{equation*}
\lim_{z \rightarrow \infty} F_1 \test{c}{a}{z} =
\lim_{z \rightarrow \infty} \frac{\Gamma(a)}{\Gamma(c)} e^z z^{c-a}
\sum_{n=0}^{\infty} \frac{(a-c)_n (1-c)_n}{\fac} z^{-n}
\end{equation*}
\end{document}

1. The first formula is made with multline*.

2. Paragraphs don't end with \\, but with an empty line.

3. No empty line must precede a display.

4. No \\ must be typed at the end of a display.

The original document probably uses zero indentation and a non zero parskip, which I don't like at all. Just uncomment the two lines in the preamble (or, better, use the parskip package).

I have also changed the definition of the macro for the hypergeometric function: the space after the vertical bar is excessive.

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And kudos for rewriting de vectoren $u_0(E), u_1(E), v(x)$ en $w(p)$ as de vectoren $u_0(E)$, $u_1(E)$,~$v(x)$ en $w(p)$! I might further be tempted to rewrite e^{\frac{xt}{t-1}} as e^{xt/(t-1)}. – Mico Dec 12 '12 at 17:31
What is it suppose to improve? It's even more work! The fraction however is shorter and cleaner :) – min Dec 12 '12 at 18:10
@Mico On second thought, I believe that $u_0(E)$, $u_1(E)$, $v(x)$~en~$w(p)$ is better. – egreg Dec 12 '12 at 18:50
@egreg - Or, how about de vectoren~$u_0(E)$, $u_1(E)$, $v(x)$ en~w(p)$? I must confess that my Dutch is rather limited; hence, I may well be missing a couple of finer points... – Mico Dec 12 '12 at 18:57 @Mico Assuming that "en" is "and", letting it go to a new line could make uncertain the reader whether the list ends with "v(x)". The tie after "vectoren" is not needed: it would be with "de vector". – egreg Dec 12 '12 at 19:01 While not reproducing exactly your first image, here is my take: \documentclass[10pt]{article} \usepackage{amsmath} \setlength{\parindent}{0pt} \newcommand{\fac}{n!} \newcommand\test[3]{\left(\begin{array}{@{\,}c@{\,}} #1 \\ #2 \end{array}\middle|\ \ #3 \right)} \begin{document} Dit gedeelte is gewijd aan de wiskundige berekening van de inproducten tussen de vectoren$u_0(E), u_1(E), v(x)$en$w(p)$. Twee bestaande formules zullen hierbij van cruciaal belang blijken te zijn. \medskip De eerste formule zegt dat \begin{multline*} \sum_{n=0}^{\infty} \frac{(a)_n}{\fac}F_1 \test{-n,b}{a}{y}_1 F_1 \test{-n}{a}{x} t^n\\ =(1-t)^{b-a}(1-t+yt)^{-b} e^{\frac{xt}{t-1}}F_1 \test{b}{a}{\textstyle\frac{xyt}{(1-t)(1- t+yt)}}, \end{multline*}% waarbij$|t| < 1\$.

\medskip
De tweede formule is de volgende benadering:
\begin{equation*}
\lim_{z \rightarrow \infty} F_1 \test{c}{a}{z} = \lim_{z \rightarrow \infty}         \frac{\Gamma(a)}{\Gamma(c)} e^z z^{c-a} \sum_{n=0}^{\infty} \frac{(a-c)_n (1-c)_n}{\fac}     z^{-n}
\end{equation*}
\end{document}


To get rid of the vertical space, I removed your explicit line breaks, and inserted \medskips.

The layout of the first equation is turned to multline*, so the first line will be flushed left, while the last line will be flushed right.

The fraction is made small with \textstyle`, although I am not convinced that this looks better.

Setting everything in 10pt Computer Modern brings it quite close to your first image.

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the parskip helps with removing the vertical space, thank you both for that. The other differences are still there. Multiline does not align it the same way as the source. If you look closely you will see that the second line begins right after the first closing bracket. The pagewidth is slightly bigger in the source, which makes it possible to fit more words into one line. As you can see with the first arrow. Both articles are 12pt, but because of the slightly different size of the screenshots they are resized. – min Dec 12 '12 at 17:58