Related papers: A generalization of Tanaka's formula

The article presents the proof of Casas-Alvero conjecture.

We prove several formulas for the distribution of positive roots.

Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of $L$-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky \&…

This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…

An equivalent but useful version on the Homological Nerve Theorem is proved.

A counter example to the main result has been communicated to the author by Matei Toma.

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation $a_{n+1} = \bigl(\alpha + \frac{\beta}{n+\gamma}\bigr) a_n$. We apply the obtained formula to several particular important sequences.…

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.

In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…

In this paper we give a short, new proof of a natural generalization of Gerzon's bound. This bound improves the Delsarte, Goethals and Seidel's upper bound in a special case. Our proof is a simple application of the linear algebra bound…

We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

We study an inequality suggested by Littlewood, our result refines a result of Bennett.