Variational minimization on the 4D singular harmonic oscillator with quartic trial functions yields the Wallis product for odd effective angular momenta and its reciprocal for even ones in the large-nu limit via Gamma-function ratios.
Lavrenov,Generalized Kustaanheimo–Stiefel transformations,N-dimensional singular oscillator and generalized MICZ–Kepler system,arXiv preprint(2019) , [1908.03572]
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Wallis Products from the Four-Dimensional Singular Harmonic Oscillator
Variational minimization on the 4D singular harmonic oscillator with quartic trial functions yields the Wallis product for odd effective angular momenta and its reciprocal for even ones in the large-nu limit via Gamma-function ratios.