Extension of Eulerʹs beta function

An extension of Eulerʹs beta function, analogous to the recent generalization of Eulerʹs gamma function and Riemannʹs zeta function, for which the usual properties and representation are naturally and simply extended, is introduced. It is proved that the extension is connected to the Macdonald, error and Whittaker functions. In addition, the extended beta distribution is introduced.