相关论文: The joy of multisection: elementary approaches to …

We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic…

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…

Ramanujan derived the well known divergent-sum of integers in more than one way. We generalise the informal method to higher powers of the Riemann zeta function through a study of the Eulerian numbers in particular. Within the context of…

We revisit several entries from Ramanujan's notebooks which follow from more elementary arguments than a first glance may suggest. Our goal is to demystify these results through more accessible proofs, while also shining some light on the…

In the first part we establish a connection between the Euler-Maclaurin summation formula and the Rota-Baxter functional equation. In the second part we give a simple proof of a formula, due to Ramanujan, on the summation of certain…

This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions…

We discuss several topics related to polylogarithms with focus on dilogarithms. The topics are: a generating function with harmonic numbers coming from Ramanujan, extending the dilogarithm to complex numbers beyond the unit disk, and…

The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form)…

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic…

We connect and generalize Matiyasevich's identity #0102 with Bernoulli numbers and an identity of Candelpergher, Coppo and Delabaere on Ramanujan summation of the divergent series of the infinite sum of the harmonic numbers. The formulae…

We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan's tau function which involves t-cores and a new class of partitions which we call (m,k)-capsids. The same method can be applied in conjunction with…

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by…

The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overpartitions via congruences in arithmetic progressions, we…

Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several…

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…

We state and prove a number of unilateral and bilateral $q$-series identities and explore some of their consequences. Those include certain generalizations of the $q$-binomial sum which also generalize the $q$-Airy function introduced by…

We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…

We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the…

A new sums-of-tails identity involving two parameters $b$ and $d$ is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from the Lost Notebook is shown to be a special case of our…

We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of…