Orthogonality with respect to a Jacobi differential operator and applications

Let μ be a finite positive Borel measure on [ − 1 , 1 ] , m a fixed natural number and L ( α , β ) [ f ] = ( 1 − x 2 ) f ″ + ( β − α − ( α + β + 2 ) x ) f ′ , with α , β > − 1 . We study algebraic and analytic properties of the sequence of monic polynomials ( Q n ) n > m that satisfy the orthogonality relations ∫ L ( α , β ) [ Q n ] ( x ) x k d μ ( x ) = 0 for all  0 ≤ k ≤ n − 1 . A fluid dynamics model for source points location of a flow of an incompressible fluid with preassigned stagnation points is also considered.