Beta function

For \(z,w\in\CC\) with \(\operatorname{Re}z>0\) and \(\operatorname{Re}w>0\), the beta function is \[ B(z,w)\coloneqq\int_0^1 t^{z-1}(1-t)^{w-1}\dt, \] where \(t^{s}\coloneqq e^{s\log t}\) for \(t>0\), with \(\log\) the real natural logarithm.