Submitted:
06 January 2026
Posted:
08 January 2026
You are already at the latest version
Abstract
This paper presents modified Lagrange-Jacobi functions derived from the sine, exponential, and hyperbolic tangent coordinate transformations. The resulting Lagrange-Jacobi functions and their respective matrix elements for observables can be reduced to their respective Lagrange-Legendre, Lagrange-Chebyshev, and Lagrange-Gegenbauer functions. Furthermore, this paper postulates that the Lagrange-mesh functions form approximate
complete set of basis, a property implied by their approximate orthogonality.
Keywords:
coordinate transformation
; lagrange-mesh method
; lagrange-jacobi functions
; exponential mesh
; hyperbolic mesh
; trigonometric mesh
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