  The classical beta function B(x; y) is one of the most fundamental special
functions, due to its important role in various fields in the mathematical,
physical, engineering and statistical sciences. Useful extensions of the
classical Beta function has been considered by many authors. In the present
paper, our main objective is to study the convergence of extensions of
classical beta function and introduce modified extension of classical beta
function. It is interpreted numerically and geometrically in the view of
convergence, further properties and integral presentations are established.
