An example of nonsymmetric semi-classical form of class \(s=1\); generalization of a case of Jacobi sequence (Q5926150)

The author gives explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class \(s=1\). This sequence generalizes the Jacobi polynomial sequence, that is, the author gives a new orthogonal sequence \(\{\widehat{P}^{(\alpha, \alpha+1)}_n(x,\mu)\}\), where \(\mu\) is an arbitrary parameter with Re\((1-\mu)>0\) in such a way that for \(\mu=0\) one has the well-known Jacobi polynomial sequence \(\{\widehat{P}^{(\alpha, \alpha+1)}_n(x)\}, n\geq 0\).