Multipoint Padé approximations of the beta function (Q1033910)

The author studies multipoint rational approximations with free poles for the beta function \[ f_{\alpha}(z)=B(a,\,z)=\frac{\Gamma(\alpha)\Gamma(z)}{\Gamma(\alpha+z)}, \] where \(\alpha\) is an arbitrary fixed complex parameter which is not an integer. The denominators of the approximations satisfy orthogonality relations with variable weight with respect to a discrete measure. The author obtains the limit distribution of the zeros of the denominators. Moreover, the author gives a potential-theoretic interpretation of the results obtained.