相关论文: Identities for hypergeometric integrals of differe…
We consider the KZ differential equations over $\mathbb C$ in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $\mathbb F_p$. We study the space…
In this paper, we define a new identity for twice differentiable mappings and obtained some new estimates on the generalization of Hadamard's and Simson's type inequalities for quasi-geometrically convex mappings using of this identity.
In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the ${}_{2} F_{1}$ hypergeometric series. By using this method, he derived almost all of the previously known hypergeometric…
In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…
Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
Some identities for the Riemann zeta-function are proved, using properties of the Mellin transform and M\"untz's identity.
In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical)…
Polynomial identities of two-dimensional Novikov algebras are studied over the complex field $\mathbb{C}$. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively…
The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures m(y^2+2xy+y-x^3-2x^2-x)=5/7*m(y^2+4xy+y-x^3+x^2) which is one of many examples that arise from the comparison of Mahler…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
Through a systematic approach on generating Wilf-Zeilberger-pairs, we prove some hypergeometric identities conjectures due to Z.W. Sun, J. Guillera and Y. Zhao etc., including two Ramanujan-$1/\pi^4$, one $1/\pi^3$ formulas as well as a…
Let A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a…
An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group S_N is presented for integer values of the parameter. The corresponding integrals…
Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…
Let $F$ be a finite field with the characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis for $\mathbb{Z}_{2}$-graded…
In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and…
In this work, we study the integrability, as well as the dynamics of the Lorenz System. This include a very useful identity:\[ \beta z^2(\sigma t)+y^2(\beta\sigma t)=\rho x^2(\beta t)+\nu e^{-2\beta\sigma t}, \]where $\nu\in\mathbb{R}$ is a…
We give multidimensional generalizations of several transformation formulae for basic hypergeometric series of a specific type. Most of the upper parameters of the series differ multiplicatively from corresponding lower parameters by a…
In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…