\(Q\)-polynomial of pretzel links (Q690151)

An explicit formula of the \(Q\)-polynomial of a pretzel link \(L(p_ 1, p_ 2, \dots, p_ n)\) is given in terms of polynomials of the form \((\lambda^ p_ + - \lambda^ p_ -)/(\lambda^ 2_ + - \lambda^ 2_ -)\) with \(\lambda_ + + \lambda_ - = x\) and \(\lambda_ + \lambda_ - = 1\). Here the \(Q\)-polynomial satisfies the skein relation \(Q(L_ +) + Q(L_ -) = xQ(L_ 0) + xQ(L_ \infty)\) for the usual skein quadruple \(L_ +\), \(L_ -\), \(L_ 0\) and \(L_ \infty\).