A probabilistic approach to some of Euler’s number theoretic identities
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- by Don Rawlings PDF
- Trans. Amer. Math. Soc. 350 (1998), 2939-2951 Request permission
Abstract:
Probabilistic proofs and interpretations are given for the $q$-binomial theorem, $q$-binomial series, two of Euler’s fundamental partition identities, and for $q$-analogs of product expansions for the Riemann zeta and Euler phi functions. The underlying processes involve Bernoulli trials with variable probabilities. Also presented are several variations on the classical derangement problem inherent in the distributions considered.References
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Additional Information
- Don Rawlings
- Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
- Email: drawling@math.calpoly.edu
- Received by editor(s): August 8, 1996
- Received by editor(s) in revised form: September 16, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 2939-2951
- MSC (1991): Primary 60K99, 11P81, 05A30, 05A17
- DOI: https://doi.org/10.1090/S0002-9947-98-01969-2
- MathSciNet review: 1422618