|
|||||
|
|
A probabilistic approach to some of Euler's number theoretic identities |
|
| Authors: | Don Rawlings |
| Affiliation: | Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407 |
| 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. |
| 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 |
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Transactions of the American Mathematical Society》下载全文 | |