Quantum mechanical derivation of the Wallis formula for π

  title={Quantum mechanical derivation of the Wallis formula for $\pi$},
  author={Tamar Friedmann and Carl R. Hagen},
  journal={Journal of Mathematical Physics},
A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions. 

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On Wallis' Formula

For example, the ratio is