Sobolev orthogonality for the Gegenbauer polynomials {Cn(−N+12)}n⩾0

In this work, we obtain the property of Sobolev orthogonality for the Gegenbauer polynomials {Cn(−N+12)}n⩾0, with N⩾1 a given nonnegative integer, that is, we show that they are orthogonal with respect to some inner product involving derivatives. The Sobolev orthogonality can be used to recover properties of these Gegenbauer polynomials. For instance, we can obtain linear relations with the classical Gegenbauer polynomials.