2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138928We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect to a differential operator and a discrete-continuous Sobolev type inner product.Classical Analysis and ODEsAnalysis of PDEs42C05 ; 33C25text