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Shift operators and recurrence relations for Legendre polynomials with noninteger associativity and definite parity

In: Physical and Mathematical Aspects of Symmetries

Author

Listed:
  • Eugenio Ley-Koo

    (Universidad Nacional Autnoma de México, Instituto de Física)

  • Salvador A. Cruz

    (Universidad Autnoma Metropolitana-Iztapalapa, Departamento de Física)

Abstract

This is the written version of new results reported at Gr31 in our contribution “O(2) Symmetry Breaking in Dihedrally Confined Atoms and Consequent Modifications of the Periodic Table”. It is focused on identifying new shift operators and recurrence relations for Legendre polynomials with noninteger asociativities and definite parities, due to the dihedral confinement and its O(2) symmetry breaking. Recurrence relations play a key role in evaluating the two-electron matrix elements of their Coulomb repulsion multipole components in the Hartree-Fock calculations for the confined atoms.

Suggested Citation

  • Eugenio Ley-Koo & Salvador A. Cruz, 2017. "Shift operators and recurrence relations for Legendre polynomials with noninteger associativity and definite parity," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 233-238, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_35
    DOI: 10.1007/978-3-319-69164-0_35
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