Typeset Kampé de Fériet function

I’m trying to reproduce the way the Kampé de Fériet function is typeset in a paper. Here’s a screenshot:

Here’s what I’ve got:

documentclass{article}

usepackage{amstext, amsmath, amssymb}

makeatletter
newcommand{longdash}[1][2em]{%
  makebox[#1]{$m@thsmash-mkern-7mucleadershbox{$mkern-2musmash-mkern-2mu$}hfillmkern-7musmash-$}}
makeatother
newcommand{omitskip}{kern-arraycolsep}
newcommand{llongdash}[1][2em]{longdash[#1]omitskip}
newcommand{rlongdash}[1][2em]{omitskiplongdash[#1]}


begin{document}

begin{equation}
F_{2:0:0}^{0:2:1}left[{llongdash :dfrac{a+b+1}{2},dfrac{a-b+1}{2};1atop dfrac{a+b+3}{2},dfrac{a-b+3}{2}:llongdash;rlongdash}Biggvert xdfrac{y^2}{4},dfrac{y^2}{4}right]
end{equation}

end{document}

which produces this:

It’s close but not quite. The subscript and subperscript appear to be slightly shifted horizontally. Worse yet, the parameters (or arguments of the function) appear to be misaligned as well. Any advise?

The long dashes were borrowed from here.

documentclass{article}

usepackage{amsmath}

newcommand{linefill}{% a variation on rightarrowfill
  {-}mkern-7mu
  cleadershbox{$mkern-2mu-mkern-2mu$}hfill
  mkern-7mu{-}%
}

begin{document}

begin{equation}
F{}_{2:0:0}^{0:2:1}
  left[
   setlength{arraycolsep}{0pt}% local assignment
   begin{array}{c@{{}:{}}c@{;{}}c}
   linefill & dfrac{a+b+1}{2},dfrac{a-b+1}{2} & quad 1 [1ex]
   dfrac{a+b+3}{2},dfrac{a-b+3}{2} & qquadlinefill & linefill
   end{array}
   ;middle|;
   xdfrac{y^2}{4},dfrac{y^2}{4}
 right]
end{equation}

end{document}

documentclass{article}

usepackage{amsmath}

begin{document}

[
  F mathstrut_{2:0;0}^{0:2;1}
    left[
      begin{array}{@{} c @{:} c @{;} c @{;}}
        dfrac{phantom{mu + nu + 3, mu - nu + 3}}{phantom{2}} & 
          dfrac{mu + nu + 1}{2}, dfrac{mu - nu + 1}{2} &
          1 
        dfrac{mu + nu + 3}{2}, dfrac{mu - nu + 3}{2} &
          dfrac{phantom{mu + nu + 1, mu - nu + 1}}{phantom{2}} &
          dfrac{phantom{0}}{phantom{0}}
      end{array}
      a dfrac{z^2}{4}, dfrac{z^2}{4}
    right]
]

end{document}