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A probabilistic approach to some of Euler's number theoretic identities
Author(s):
Don
Rawlings
Journal:
Trans. Amer. Math. Soc.
350
(1998),
2939-2951.
MSC (1991):
Primary 60K99, 11P81, 05A30, 05A17
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Abstract:
Probabilistic proofs and interpretations are given for the  -binomial theorem,  -binomial series, two of Euler's fundamental partition identities, and for  -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:
10.1090/S0002-9947-98-01969-2
PII:
S 0002-9947(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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