\(N\)-dimensional harmonic oscillator yields monotonic series for the mathematical constant \(\pi\)

DOI10.1016/0377-0427(90)90021-QzbMath0702.65019OpenAlexW2038891292MaRDI QIDQ915352

R. Lynch, Harry A. Mavromatis

Publication date: 1990

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90021-q

zbMATH Keywords

harmonic oscillatorseries for pi

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Computation of special functions and constants, construction of tables (65D20) Evaluation of number-theoretic constants (11Y60)

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An interesting new result involving associated laguerre polynomials ⋮ The wallis formula for PI, including two new expressions involving irrationals ⋮ Some comprehensive expressions forπand 1/π ⋮ Two new associated Laguerre integral results ⋮ Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case

Cites Work

• Two doubly infinite sets of series for \(\pi\)
• An explicit cubic iteration for \(\pi\)
• Spherical harmonics
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