Here's the Mathematica version:

PrBbeatsA[\[Alpha]a_, \[Beta]a_, \[Alpha]b_, \[Beta]b_] := \!\( \UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\[Alpha]b\)] \FractionBox[\(Beta[\[Alpha]a + i, \[Beta]b + \[Beta]a]\), \(\((\[Beta]b + i)\) Beta[ 1 + i, \[Beta]b] Beta[\[Alpha]a, \[Beta]a]\)]\)