Related papers: Pentagon Identity Revisited I

We extend the well-known word analogy task to a one-to-X formulation, including one-to-none cases, when no correct answer exists. The task is cast as a relation discovery problem and applied to historical armed conflicts datasets,…

We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an…

These notes deal with a few properties of convolutions in the role of approximations to the identity.

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.

We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

In this paper, we first propose a cohomological derivation of the celebrated Euler's Pentagonal Number Theorem. Then we prove an identity that corresponds to a bosonic extension of the theorem. The proof corresponds to a cohomological…

A quantity that promises to reveal important information on perturbative and non-perturbative QCD dynamics is the azimuthal decorrelation between jets in different hard processes. In order to access this information fixed-order NLO…

A refinement of the q-trinomial coefficients is introduced, which has a very powerful iterative property. This ``T-invariance'' is applied to derive new Virasoro character identities related to the exceptional simply-laced Lie algebras…

In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant.…

We give an overview about the power product expansion of the exponential series and derive some q-analogs

We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed…

In this paper we give new identities involving q-Euler polynomials of higher order.

A classical analogue of the Adlam-Kent "Quantum paradox of choice" (arXiv:1509.04226) is presented.

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…

In this paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…

I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic…

Recently the possible origin of the so-called quark-lepton complementarity relations has received a considerable amount of attention. We point out some of the inherent ambiguities in such analyses.

A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.

We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining…