Formula for correcting ABV (Alcohol by volume)

Feb 2017
Czech Republic
can anyone help me find formula, which would correct ABV, that is measured by alcoholmeter, which is calibrated for 20°C, but the mixture has different temperature?

I want to implement this calculation into program so I can not use alcoholometric tables.

I know this formula for density of mixture at 20°C, can it help me?

So e.g. I have measured 50%ABV at 10°C, tables would give me real ABV ==> 53,7%. Now I need to calculate this by formula. I will be very thankful for any help.

Thank you