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I am trying to align my equation number to be vertically centre to the equation. How can I go about doing this? I have attached a screenshot of my output.

I am using pdfLaTex+MakeIndex+BibTeX as me Latex processor if that could possibly make a difference.

Here is my code,

documentclass[a4paper, 11pt, leqno]{article}

usepackage{amsmath}

usepackage{amsfonts}

usepackage{indentfirst}

usepackage{hyperref}

usepackage{bigints}



setlength{parindent}{0em}

setlength{parskip}{1em}



begin{document}



par

This is some text.

begin{equation} label{cyclicFourierTransform}

begin{split}

centerline{$F(s) = bigints_{-infty}^{infty} f(x)e^{-i2{pi}xs};mathrm{d}x$} \

centerline{$f(x) = bigints_{-infty}^{infty} F(s)e^{-i2{pi}xs};mathrm{d}s$}

end{split}

end{equation}



par

This is some more text.



end{document}

And here is my output,

Thank you in advance!

I'd use aligned instead of split and normal ints instead of bigints. Also, as others pointed out, remove centerline and consider not using it in LaTeX at all.

documentclass[a4paper, 11pt, leqno]{article}

usepackage{amsmath}

usepackage{amsfonts}

usepackage{indentfirst}

usepackage{hyperref}

usepackage{bigints}



setlength{parindent}{0em}

setlength{parskip}{1em}



begin{document}



This is some text.

begin{equation} label{cyclicFourierTransform}

begin{aligned}

F(s) &= int_{-infty}^{infty} f(x)e^{-i2{pi}xs};mathrm{d}x \

f(x) &= int_{-infty}^{infty} F(s)e^{-i2{pi}xs};mathrm{d}s

end{aligned}

end{equation}



This is some more text.



end{document}

Not sure why you're complicating things.

documentclass[a4paper, 11pt, leqno]{article}

usepackage{amsmath}

usepackage{amsfonts}

usepackage{indentfirst}

usepackage[skip=1em]{parskip}

usepackage{hyperref}



newcommand{diff}{mathop{}!mathrm{d}}



begin{document}



par

This is some text.

begin{equation} label{cyclicFourierTransform}

begin{split}

F(s) &= int_{-infty}^{infty} f(x)e^{-i2{pi}xs}diff x \

f(x) &= int_{-infty}^{infty} F(s)e^{-i2{pi}xs}diff s

end{split}

end{equation}

This is some more text.



end{document}

Note the better definition for the differential operator (I'd prefer an italic d, though; with this setup, you can change it just once for the whole document).

The parskip package is better if you really want to use vertical space between paragraphs. Again, just commenting out the call to the package allows for switching to traditional typesetting. The package makes also some other fixes that manual setting doesn't perform. I left 1em, but it's not really a good unit to use here.

If you remove centerline you get

documentclass[a4paper, 11pt, leqno]{article}

usepackage{amsmath}

usepackage{amsfonts}

usepackage{indentfirst}

usepackage{hyperref}

usepackage{bigints}



setlength{parindent}{0em}

setlength{parskip}{1em}



begin{document}



par

This is some text.

begin{equation} label{cyclicFourierTransform}

begin{split}

F(s) = bigints_{-infty}^{infty} f(x)e^{-i2{pi}xs};mathrm{d}x \

f(x) = bigints_{-infty}^{infty} F(s)e^{-i2{pi}xs};mathrm{d}s

end{split}

end{equation}



par

This is some more text.



end{document}

Or an arguably cleaner version with inputs from David Carlisle.

documentclass[a4paper, 11pt, leqno]{article}

usepackage{amsmath}

usepackage{amsfonts}

usepackage{indentfirst}

usepackage{hyperref}

usepackage{bigints}



setlength{parindent}{0em}

setlength{parskip}{1em}



begin{document}



This is some text.

begin{equation} label{cyclicFourierTransform}

begin{split}

F(s) = intlimits_{-infty}^{infty} f(x),mathrm{e}^{-mathrm{i}2{pi}xs},mathrm{d}x \

f(x) = intlimits_{-infty}^{infty} F(s),mathrm{e}^{-mathrm{i}2{pi}xs},mathrm{d}s

end{split}

end{equation}



This is some more text.



end{document}