Related papers: Hypergeometric accelerations with shifted indices
The Kaczmarz method is an iterative numerical method for solving large and sparse rectangular systems of linear equations. Gearhart, Koshy and Tam have developed an acceleration technique for the Kaczmarz method that minimizes the distance…
This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integrals to Zeilberger's creative telescoping for parameterized…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
Using a ${}_7F_6$ hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long…
In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those…
The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results…
By applying Slater's transformation formulas for the bilateral basic hypergeometric series ${}_2\psi_{2}$, we derive three type translation formulas for the generalized Zwegers' $\mu$-function (``continuous $q$-Hermite function'') which was…
In PRL 115, 143001 (2015), H. Mera et al. developed a new simple but precise Hypergeometric Resummation technique. In this work, we suggest to obtain half of the parameters of the Hypergeometric function from the strong coupling expansion…
In this article, we introduce an innovative parametric representation of the Hubble parameter, providing a model-independent means to explore the dynamics of an accelerating cosmos. The model's parameters are rigorously constrained through…
Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured by Guo and Schlosser and recently confirmed by Jana and…
In a seminal work of Zhang and Sra, gradient descent methods for geodesically convex optimization were comprehensively studied. In particular, Zhang and Sra derived a comparison inequality that relates the iterative points in the…
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our…
Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provide similar expansion results for averages involving…
The first known $q$-analogues for any of the $17$ formulas for $\frac{1}{\pi}$ due to Ramanujan were introduced in 2018 by Guo and Liu (J. Difference Equ. Appl. 29:505-513, 2018), via the $q$-Wilf-Zeilberger method. Through a…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…
In Part I of the present series of papers, we adumbrate our idea of Riemannian geometry to higher order in the infinitesimals and derive expressions for the appropriate generalizations of parallel transport and the Riemannian curvature…
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions. The main result is that the convolution of most arithmetic functions…
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…
Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's ${}_6\psi_6$ bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the…
We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative ``Bailey chain'' concept in the setting of basic hypergeometric series very well-poised on unitary $A_{\ell}$ or symplectic $C_{\ell}$…