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Analytical equations for an infinite series involving low-order associated Legendre functions in geoscience
https://orcid.org/0000-0003-0737-1827
Abstract The associated Legendre functions constituting the kernel function of spherical harmonics have a wide range of applications in geodesic and geophysical fields, such as calculating the Green’s functions for a spherical Earth model. The analytical expressions for the infinite series involving the associated Legendre functions are useful. In this paper, starting with the generating function, we present a set of analytical equations for an infinite series involving associated low-order $$\left( {m = 0,~1,~2} \right)$$ Legendre functions. After careful verification, the accuracy and effectiveness of the nearly sixty listed equations are confirmed. The open-source code written using the Wolfram language, GNU octave/MATLAB, and Fortran-90 are available through GitHub (https://github.com/UCAStanghe2014/analytical_sums_associated_Legendre).
Analytical equations for an infinite series involving low-order associated Legendre functions in geoscience
https://orcid.org/0000-0003-0737-1827
Abstract The associated Legendre functions constituting the kernel function of spherical harmonics have a wide range of applications in geodesic and geophysical fields, such as calculating the Green’s functions for a spherical Earth model. The analytical expressions for the infinite series involving the associated Legendre functions are useful. In this paper, starting with the generating function, we present a set of analytical equations for an infinite series involving associated low-order $$\left( {m = 0,~1,~2} \right)$$ Legendre functions. After careful verification, the accuracy and effectiveness of the nearly sixty listed equations are confirmed. The open-source code written using the Wolfram language, GNU octave/MATLAB, and Fortran-90 are available through GitHub (https://github.com/UCAStanghe2014/analytical_sums_associated_Legendre).
Analytical equations for an infinite series involving low-order associated Legendre functions in geoscience
https://orcid.org/0000-0003-0737-1827
Abstract The associated Legendre functions constituting the kernel function of spherical harmonics have a wide range of applications in geodesic and geophysical fields, such as calculating the Green’s functions for a spherical Earth model. The analytical expressions for the infinite series involving the associated Legendre functions are useful. In this paper, starting with the generating function, we present a set of analytical equations for an infinite series involving associated low-order $$\left( {m = 0,~1,~2} \right)$$ Legendre functions. After careful verification, the accuracy and effectiveness of the nearly sixty listed equations are confirmed. The open-source code written using the Wolfram language, GNU octave/MATLAB, and Fortran-90 are available through GitHub (https://github.com/UCAStanghe2014/analytical_sums_associated_Legendre).
Analytical equations for an infinite series involving low-order associated Legendre functions in geoscience
Tang, He (author) / Sun, Wenke (author)
Journal of Geodesy ; 95
2021
Article (Journal)
Electronic Resource
English
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