Euler’s reflection formula, infinite product formulas, and the correspondence principle of quantum mechanics
- 1 June 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (6), 063504
- https://doi.org/10.1063/5.0030945
Abstract
We generalize the derivation of the Wallis formula for π from a variational computation of the spectrum of the hydrogen atom. We obtain infinite product formulas for certain combinations of gamma functions, which include irrational numbers such as as well as some nested radicals. We also derive Euler’s reflection formula for reciprocals of positive even integers. We show that Bohr’s correspondence principle allows us to derive our product formulas and the reflection formula without the need for the limit definition of the gamma function.
Funding Information
- National Science Foundation (MCTP-1143716)
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