Related papers: 50 Years of Bailey's lemma
The Rogers-Ramanujan identity for $\!\!\phantom{|}_1\psi_1$ $$ \sum_{n\in\mathbb{Z}} \frac{(a;q)_n}{(b;q)_n} z^n\;=\; \frac{(q,b/a,az,q/az;q)_\infty}{(b,q/a,z,b/az;q)_\infty} $$ can be classified as one related to the Bethe Ansatz for…
I present here a collection of formulas inspired from the Ramanujan Notebooks. These formulas were found using an experimental method based on three widely available symbolic computation programs: PARI-Gp, Maple and Mathematica. A new…
This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…
Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
This is a 1971 dissertation. Only its extended abstract was published at the time. While some results appeared in other publications, a number of details remained unpublished and may still have relevance.
Ramanujan made many beautiful and elegant discoveries in his short life of 32 years, and one of them that has attracted the attention of several mathematicians over the years is his intriguing formula for $\zeta(2n+1)$. To be sure,…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
For any rational number $p_0\ge 2$ we prove an identity of Rogers-Ramanujan's type. Bijection between the space od states for $XXZ$ model and that of $XXX$ model is constructed
A chapter in a book"50 years of QGP" An extended summary of the field can be found in large books and reviews, e.g., my take in Ref.~\cite{Shuryak:2024zrh}. It is hard to compress its 600+ pages and 50+ years of research to a few given…
In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists for over 50 years. A version of this note also serves as an…
This is the classical monograph on the combinatorial study of Eulerian polynomials, published in 1970. It has been retyped in TeX and made available on the web with the kind permission of Springer-Verlag. This on-line version has an ouput…
Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain $q$-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement…
We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [1991, A log-linear…
Let $(\alpha_n(a,k),\beta_n(a,k))$ be a WP-Bailey pair. Assuming the limits exist, let \[ (\alpha_n^*(a),\beta_n^*(a))_{n\geq 1} = \lim_{k \to 1}\left(\alpha_n(a,k),\frac{\beta_n(a,k)}{1-k}\right)_{n\geq 1} \] be the \emph{derived}…
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of G\"ollnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at…
We extend the table of Garoufalidis, Le and Zagier concerning conjectural Rogers-Ramanujan type identities for tails of colored Jones polynomials to all alternating knots up to 10 crossings. We then prove these new identities using q-series…