How do I flush a piece of an equation to the right?

Question

I have the following expression

\begin{dmath}
    \int_0^1 y^{\frac{\dd-\ell}{2}-\dd_\p+s-1} (1-y)^{2\dd_\p-h+\ell-1}\\
    \pFq{2}{1}{s,s+j}{2s+j}{1-y}
    \pFq{2}{1}{-h+\frac{\dd+\ell}{2}+\dd_\p,-h+\frac{\dd+\ell}{2}+\dd_\p}{\dd-h+1}{y}
    \diff y\,.
\end{dmath}

This gives the following which looks very ugly.

Is there a way to flush the Hypergeometric functions a bit to the left? Thanks.

Answer 1

You can get the first hypergeometric aligned with the integral symbol:

\documentclass{article}
\usepackage{amsmath}
\usepackage{showframe}
\ExplSyntaxOn
% https://tex.stackexchange.com/a/125531/4427
\NewDocumentCommand{\pFq}{O{}mmmmm}
 {
  % #2 = left subscript, #3 = right subscript
  % #4 = top, #5 = bottom, #6 = right
  \group_begin:
  \keys_set:nn { hypergeometric } { #1 }
  \hypergeometric_print:nnnnn { #2 } { #3 } { #4 } { #5 } { #6 }
  \group_end:
 }
\NewDocumentCommand{\hypergeometricsetup}{m}
 {
  \keys_set:nn { hypergeometric } { #1 }
 }
\tl_new:N \l_hypergeometric_divider_tl
\tl_new:N \l_hypergeometric_left_tl
\tl_new:N \l_hypergeometric_right_tl
\keys_define:nn { hypergeometric }
 {
  symbol .tl_set:N = \l_hypergeometric_symbol_tl,
  symbol .initial:n = F,
  separator .tl_set:N = \l_hypergeometric_separator_tl,
  separator .initial:n = {},
  skip .tl_set:N = \l_hypergeometric_skip_tl,
  skip .initial:n = 8,
  divider .choice:,
  divider/semicolon .code:n = \tl_set:Nn \l_hypergeometric_divider_tl { ;; },
  divider/bar .code:n = \tl_set:Nn \l_hypergeometric_divider_tl { ;\middle|; },
  divider .initial:n = semicolon,
  fences .choice:,
  fences/brack .code:n = 
   \tl_set:Nn \l_hypergeometric_left_tl {[}
   \tl_set:Nn \l_hypergeometric_right_tl {]},
  fences/parens .code:n = 
   \tl_set:Nn \l_hypergeometric_left_tl {(}
   \tl_set:Nn \l_hypergeometric_right_tl {)},
  fences .initial:n = brack,
 }
\cs_new_protected:Nn \hypergeometric_print:nnnnn
 {
  % the main symbol
  {} \sb {#1} \l_hypergeometric_symbol_tl \sb { #2 }
  % the parameters
  \left\l_hypergeometric_left_tl
  \genfrac .. % no delimiters
           {0pt} % no line
           {} % default style
           { __hypergeometric_process:n { #3 } } % numerator
           { __hypergeometric_process:n { #4 } } % denominator
  \l_hypergeometric_divider_tl
  #5
  \right\l_hypergeometric_right_tl
 }
\cs_new_protected:Nn __hypergeometric_process:n
 {
  \clist_use:nn { #1 }
   {
    {\l_hypergeometric_separator_tl}
    \mspace { \l_hypergeometric_skip_tl mu }
   }
 }
\ExplSyntaxOff
\hypergeometricsetup{
  fences=brack,
  divider=semicolon,
  separator={,},
}
\newcommand{\diff}{\mathop{}!d}
\newcommand{\dd}{\Delta}
\newcommand{\p}{\phi}
\begin{document}
\begin{equation}
\begin{split}
&!
 \int_0^1 y^{\frac{\dd-\ell}{2}-\dd_\p+s-1} (1-y)^{2\dd_\p-h+\ell-1}\
& \pFq{2}{1}{s,s+j}{2s+j}{1-y}
 \pFq{2}{1}{-h+\frac{\dd+\ell}{2}+\dd_\p,-h+\frac{\dd+\ell}{2}+\dd_\p}{\dd-h+1}{y}
 \diff y,.
\end{split}
\end{equation}
\end{document}

If you want the number aligned with the bottom row, use the tbtags option to amsmath: with \usepackage[tbtags]{amsmath} you'd get

Alternatively, if you want such placement only for this display and not generally for split, you can use aligned:

\begin{equation}
\begin{aligned}[b]
&\!
 \int_0^1 y^{\frac{\dd-\ell}{2}-\dd_\p+s-1} (1-y)^{2\dd_\p-h+\ell-1}\\
& \pFq{2}{1}{s,s+j}{2s+j}{1-y}
 \pFq{2}{1}{-h+\frac{\dd+\ell}{2}+\dd_\p,-h+\frac{\dd+\ell}{2}+\dd_\p}{\dd-h+1}{y}
 \diff y\,.
\end{aligned}
\end{equation}

Another possibility worth mentioning is to give a name to the complicated formula:

If we set
\[
 H(y)=
 \pFq{2}{1}{s,s+j}{2s+j}{1-y}
 \pFq{2}{1}{-h+\frac{\dd+\ell}{2}+\dd_\p,-h+\frac{\dd+\ell}{2}+\dd_\p}{\dd-h+1}{y},
\]
then we can consider
\begin{equation}
 \int_0^1 y^{\frac{\dd-\ell}{2}-\dd_\p+s-1} (1-y)^{2\dd_\p-h+\ell-1} H(y)\diff y,
\end{equation}

Fill in with the appropriate wording.

Answer 2

How about placing the first hypergeometric term on the first row?

Note that I've rewritten \frac{\dd-\ell}{2} and \frac{\dd+\ell}{2} as (\dd-\ell)/2 and (\dd+\ell)/2, respectively.

\documentclass{article}
\usepackage{amsmath} % for 'multline*' env.
% Some macro definitions:
\providecommand\dd{\Delta}
\providecommand\p{\phi}
\providecommand\pFq[5]{{}{#1}F{#2} \Bigl[ 
   \begin{matrix} #3 \ #4\end{matrix} ,;, #5 \Bigr]}
\providecommand\diff{,\mathrm{d}}
\providecommand\zzz{-h+(\dd+\ell)/2+\dd_\p}
\begin{document}
\begin{multline}
    \int_0^1 y^{(\dd-\ell)/2-\dd_\p+s-1}, 
    (1-y)^{2\dd_\p-h+\ell-1},
    \pFq{2}{1}{s,\ s+j}{2s+j}{1-y} \[\jot]
    \pFq{2}{1}{\zzz,\ \zzz}{\dd-h+1}{y}
    \diff y,.
\end{multline}
\end{document}