Quick construction of recurrence relations for the Jacobi coefficients (Q1195744)

The author presents recurrence relations for the Jacobi series coefficients of functions. Differential equations up to fourth order are studied. Some useful considerations are made for fourth-order differential equations. Two illustrative examples are given and completely studied and both are connected with the \((n-1)\)-th associated Jacobi polynomial \(W_{n-1}^{(\alpha,\beta)}\).