Related papers: Comment on `A general integral identity'

A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.

We present the evaluation of a family of logarithmic integrals. This provides a unified proof of several formulas in the classical table of integrals by I. S. Gradshteyn and I. M. Rhyzik.

In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a ${}_{2}F_{1}$-series identity with two free parameters, which was proved by Ebisu (2013), Chu (2017), and Campbell (2023) in different ways. In…

General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral…

We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.

We obtain the lens integral pentagon identity for three-dimensional mirror dual theories in terms of hyperbolic hypergeometric functions via reduction of equality for $\mathcal N=2$ lens supersymmetric partition functions of a certain…

We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…

In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well as double covers of symplectic groups. The first identity can be viewed as an extension of the doubling construction introduced…

An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to…

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

We prove the formula for the second order "thick" distributional derivative of 1/r in 3 dimensional Euclidean space. This formula generalizes the well known Frahm formulas for the distributional derivatives of 1/r.

A paper for general audience about descriptive inner model theory.

We give generalizations and simple proofs of some $q$-identities of Dilcher, Fu and Lascoux related to divisor functions.

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

Comment on ``Lancaster Probabilities and Gibbs Sampling'' [arXiv:0808.3852]

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the…

An elementary proof of an entry in the table of integrals by Gradshteyn and Rhyzik is presented.

In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.

We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…

A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given…