Trigonometric Lagrange-Jacobi functions

Abstract

This paper presents a class of trigonometric Lagrange-mesh functions constructed from the Lagrange-Jacobi functions. These functions extend the set of trigonometric Lagrange-mesh functions to beyond only those constructed directly from the sine and cosine functions. Trigonometric Lagrange-Chebyshev functions obtained from the presented trigonometric Lagrange-Jacobi functions are equivalent to known trigonometric Lagrange-Chebyshev functions constructed directly from the sine and cosine functions and generate identical matrix elements for the kinetic energy operator.