Narrow Results

We use the “tridiagonal representation approach” to solve the time-independent Schrödinger equation for the bound states of generalized versions of the trigono-metric and hyperbolic Pöschl–Teller potentials. These new solvable potentials do not belong to the conventional class of exactly solvable problems. The solutions are finite series of square integrable functions written in terms of the Jacobi polynomial.

This is the second of a series devoted to the direct and inverse approximation theorems of the p-version of the finite element method in the framework of the weighted Besov spaces. In this paper, we combine the approximability of singular solutions in the Jacobi-weighted Besov spaces, which were analyzed in the previous paper,⁴ with the technique of partition of unity in order to prove the optimal rate of convergence of the p-version of the finite element method for elliptic boundary value problems on polygonal domains.

Let be the Jacobi polynomial of degree n. For and 0 ≤ θ ≤ π , it is proved that