Related papers: A trigonometric approach to an identity by Ramanuj…
Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan…
We find new hypergeometric identities which, in a certain aspect, are stron-ger than others of the same style found by the author in a previous paper. The identities in Section \ref{section-pi} are related to some Ramanujan-type series for…
Our main results are a WZ-proof of a new Ramanujan-like series for $1/\pi^2$ and a hypergeometric identity involving three series.
We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G. E. Andrews. Several authors provided proofs of this identity, most of them rather involved or else relying on sophisticated number theoretical…
In this article we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples we will give the value of some double and triple integrals. Then, we prove several classical integral formulas with the…
It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, \emph{Proc. London Math Soc. (2)} \textbf{54} (1952),…
We generalize the "motivated proof" of the Rogers-Ramanujan identities given by Andrews and Baxter to provide an analogous "motivated proof" of Gordon's generalization of the Rogers-Ramanujan identities. Our main purpose is to provide…
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…
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our…
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical Society}, notebooks, Quarterly Reports to the University of…
We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give…
A new type of polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.
We prove a theorem which add a new member to Rogers-Ramanujan identities. This new member counts partitions with different type of constraints on even and odd parts. Generalizing this theorem, we obtain two family of partition identities of…
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial…
Inspired by the work of S. Ramanujan, many people have studied generalized modular equations and the numerous identities found by Ramanujan. These identities known as modular equations can be transformed into polynomial equations. There is…
This is an elementary explanation of a cubic composition formula due to Ramanujan.
This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…
We give an algebraic identity for cubic polynomials which generalizes Brahmagupta's identity and facilitates arithmetic in cubic fields. We also pose a question about a relationship between the elements of a cubic field of fixed trace and…
Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.
We prove four new Rogers-Ramanujan-type identities for double series. They follow from the classical Rogers-Ramanujan identities using the constant term method and properties of Rogers-Szeg\H{o} polynomials.