Asymptotic Bessel-function expansions for Legendre and Jacobi functions
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DOI: 10.1063/1.5030869
Abstract: We present new asymptotic series for the Legendre and Jacobi functions of the first and second kinds in terms of Bessel functions with appropriate arguments. The results are useful in the context of scattering problems,… read more here.
Keywords: bessel; legendre jacobi; asymptotic bessel; bessel function ... See more keywords
Groups, Jacobi functions, and rigged Hilbert spaces
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DOI: 10.1063/1.5138238
Abstract: This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations… read more here.
Keywords: harmonics; special functions; groups jacobi; rigged hilbert ... See more keywords
A Spectral Approach to Solve High-Order Ordinary Differential Equations: Improved Operational Matrices for Exponential Jacobi Functions
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DOI: 10.3390/math13193154
Abstract: This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of this… read more here.
Keywords: differential equations; jacobi functions; ordinary differential; exponential jacobi ... See more keywords