On polar Legendre polynomials (Q618679)

Let \(L_n\) be the monic Legendre polynomials. Define polynomials \(P_n\) satisfying the relation \[ (n+1)L_{n}(z)=((z-\theta)P_n(z))' = P_n(z)+ (z-\theta)P_n'(z), \] called the \(n\)-th polar Legendre polynomials. In the present paper, the authors study algebraic, differential and asymptotic properties and the zeros of these new polynomials.