相关论文: A Multiple Integral Explicit Evaluation Inspired b…

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\v{e}k states that by inserting all cyclic permutations of some initial blocks of 2's into the multiple zeta value $ \zeta(1,3,\ldots,1,3) $ and summing, one obtains…

In this paper, we develop an elementary proof of the change of variables in multiple integrals. Our proof is based on an induction argument. Assuming the formula for (m-1)-integrals, we define the integral over hypersurface in Rm, establish…

Examples show that integral forms can be efficiently proved positive semidefinite by the WDS method, but it was unknown that how many steps of substitutions are needed, or furthermore, which integral forms is this method applicable for. In…

We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.

Using the WZ-method we find some of the easiest Ramanujan's formulae and also some new interesting Ramanujan-like sums.

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…

Based on Jensen formulae and the second kind of Chebyshev polynomials, another proof is presented for an extension of a curious binomial identity due to Z. W. Sun and K. J. Wu.

Riemann zeta values are generalized to multiple zeta values (MZVs) by use of nested sums, and MZVs are generalized to regularized multiple zeta values (RMZVs) by regularization of divergent infinite series. In the present paper, we prove…

In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

In this note, we will give a short proof of an identity for cubic partitions.

We prove two explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. We define "combinatorial Hodge integrals" from these numbers in the spirit of the celebrated ELSV formula. The obtained results imply some explicit…

We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…

Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate…

In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.

We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this…

We extend the lift application for automorphic induction defined by an identity of characters to all elliptic representations.

Formal multiple zeta values allow to study multiple zeta values by algebraic methods in a way that the open question about their transcendence is circumvented. In this note we show that Hoffman's basis conjecture for formal multiple zeta…

We interpret part of the experimental results of Shwartz-Ziv and Tishby [2017]. Inspired by these results, we established a conjecture of the dynamics of the machinary of deep neural network. This conjecture can be used to explain the…

We consider a generalisation of a definite integral involving the Bessel function of the first kind. It is shown that this integral can be expressed in terms of the Fox-Wright function ${}_p\Psi_q(z)$ of one variable. Some consequences of…