A generating function for Laguerre–Sobolev orthogonal polynomials Original Research Article

Let {Sn} denote the sequence of polynomials orthogonal with respect to the Sobolev inner product(f,g)S=∫0+∞f(x)g(x)xαe−x dx+λ∫0+∞f′(x)g′(x)xαe−x dx,where α>−1, λ>0 and the leading coefficient of the Sn is equal to the leading coefficient of the Laguerre polynomial Ln(α). In this work, a generating function for the Sobolev–Laguerre polynomials is obtained.