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A probabilistic approach to some of Euler's number theoretic identities


Author: Don Rawlings
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
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: https://doi.org/10.1090/S0002-9947-98-01969-2
Keywords: Euler's process, Euler's partition identities, $q$-binomial theorem, $q$-Poisson distribution, $q$-derangement problem, $q$-Riemann zeta function, $q$-Euler phi function
Received by editor(s): August 8, 1996
Received by editor(s) in revised form: September 16, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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