Are the Eigenvalues of Banded Symmetric Toeplitz Matrices Known in Almost Closed Form?

Sven-Erik Ekström, Carlo Garoni, Stefano Serra Capizzano. Are the Eigenvalues of Banded Symmetric Toeplitz Matrices Known in Almost Closed Form?. Experimental Mathematics, 27(4):478-487, 2018. [doi]

@article{EkstromGS18,
  title = {Are the Eigenvalues of Banded Symmetric Toeplitz Matrices Known in Almost Closed Form?},
  author = {Sven-Erik Ekström and Carlo Garoni and Stefano Serra Capizzano},
  year = {2018},
  doi = {10.1080/10586458.2017.1320241},
  url = {https://doi.org/10.1080/10586458.2017.1320241},
  researchr = {https://researchr.org/publication/EkstromGS18},
  cites = {0},
  citedby = {0},
  journal = {Experimental Mathematics},
  volume = {27},
  number = {4},
  pages = {478-487},
}