A note on the Koekoeks' differential equation for generalized Jacobi polynomials
For \(\alpha,\beta > -1\) and \(M,N \geq 0\), let \(\{ P_n^{\alpha,\beta,M,N}(x) \}_{n=0}^{\infty}\) be the polynomials orthogonal on \([-1,1]\) with respect to \[ {\Gamma(\alpha+\beta+2) \over 2^{\alpha + \beta + 1} \Gamma(\alpha+1) \Gamma(\beta+1)} (1-x)^{\alpha} (1+x)^{\beta} + M\delta (x+1) + N \delta(x-1). \] The author gives simple and direct proofs of the result of J. Koekoek and R. Koekoek that these polynomials satisfy a specific differential equation of finite order provided \(\alpha\) is a nonnegative integer when \(N >0\) and \(\beta\) is a nonnegative integer when \(M>0\).
scientific article; zbMATH DE number 1423310