In the paper, a new method is presented to obtain a closed form of the generalized Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.
[1] W.N. Bailey, Generalized Hypergeometric Series, Stechert-Hafner Services Agency, New York and London, 1964.
[2] I. Iglewska-Nowak and P. Stefaniak, Wavelet based solutions to the Poisson and the Helmholtz equations on the n-dimensional unit sphere, J. Fourier Anal. Appl. 29 (2023), no. 3, Paper No. 28, 22 pp.
[3] N. Shimakura, Partial differential operators of elliptic type, Translations of Mathematical Monographs, Vol. 99, Amer. Math. Soc., Providence, Rhode Island, 1992.
Iglewska-Nowak, I. (2026). On the Green's function for the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere. Computational Methods for Differential Equations, 14(3), 1471-1477. doi: 10.22034/cmde.2025.61973.2701
MLA
Iglewska-Nowak, I. . "On the Green's function for the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere", Computational Methods for Differential Equations, 14, 3, 2026, 1471-1477. doi: 10.22034/cmde.2025.61973.2701
HARVARD
Iglewska-Nowak, I. (2026). 'On the Green's function for the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere', Computational Methods for Differential Equations, 14(3), pp. 1471-1477. doi: 10.22034/cmde.2025.61973.2701
CHICAGO
I. Iglewska-Nowak, "On the Green's function for the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere," Computational Methods for Differential Equations, 14 3 (2026): 1471-1477, doi: 10.22034/cmde.2025.61973.2701
VANCOUVER
Iglewska-Nowak, I. On the Green's function for the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere. Computational Methods for Differential Equations, 2026; 14(3): 1471-1477. doi: 10.22034/cmde.2025.61973.2701