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In this paper we investigate some Korovkin type approximation properties of the q-Meyer-K\"onig and Zeller operators and Durrmeyer variant of the q-Meyer-K\"onig and Zeller operators via Abel summability method which is a…

Functional Analysis · Mathematics 2019-04-26 Dilek Söylemez , Mehmet Ünver

In this article, we introduce and study accelerated Landweber methods for linear ill-posed problems obtained by an alteration of the coefficients in the three-term recurrence relation of the \nu-methods. The residual polynomials of the…

Numerical Analysis · Mathematics 2012-12-21 Wolfgang Erb

We show how to prove the examples of a paper by Chu and Zhang using the WZ-algorithm.

Number Theory · Mathematics 2019-06-05 Jesús Guillera

We extend Petkov\v{s}ek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems $\tau(Y) = M Y$, with $M \in {\rm GL}_n(C(x))$, where $\tau$ is the shift operator. Hypergeometric…

Symbolic Computation · Computer Science 2025-03-26 Moulay Barkatou , Mark van Hoeij , Johannes Middeke , Yi Zhou

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…

Classical Analysis and ODEs · Mathematics 2019-08-15 Yasushi Kajihara

We obtain addition formulas for $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with general parameters. These are utilized in conjunction with integral representations of these functions to derive Kummer- and Euler-type…

Classical Analysis and ODEs · Mathematics 2020-01-14 Krishna Choudhary

This study offers a comprehensive reconstruction of $f(T)$ gravity model with three distinct non-linear as well as novel forms employing a hybrid scale factor to depict the expansion history of the universe starting from early decelerated…

General Relativity and Quantum Cosmology · Physics 2026-02-17 Suraj Kumar Behera , Pratik P. Ray

The pseudo-Gamma function is a key tool introduced recently by Cheng and Albeverio in the proof of \break the density hypothesis. This function is doubly symmetric, which means that it is reflectively symmetric about the real axis by the…

Number Theory · Mathematics 2022-09-14 Yuanyou Cheng , Gongbao Li , Juping Wang

Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…

Optimization and Control · Mathematics 2021-12-30 Shengjie Xu

This paper presents an approach to summing a few families of infinite series involving hyperbolic functions, some of which were first studied by Ramanujan. The key idea is based on their contour integral representations and residue…

Number Theory · Mathematics 2024-09-27 Ce Xu , Jianqiang Zhao

This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in the setting of partial flag varieties of…

Representation Theory · Mathematics 2018-08-06 Huanchen Bao , Jonathan Kujawa , Yiqiang Li , Weiqiang Wang

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…

Combinatorics · Mathematics 2025-01-30 Kam Cheong Au

Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$. In a…

Symbolic Computation · Computer Science 2012-05-31 Johannes Bluemlein , Sebastian Klein , Carsten Schneider , Flavia Stan

The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…

Algebraic Geometry · Mathematics 2013-06-11 Roxana Bujack , Gerik Scheuermann , Eckhard Hitzer

We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that $k$ is the summation index. By setting a parameter $x$ to $xq^n$, we may find a recurrence relation of the summation by using the…

Combinatorics · Mathematics 2007-05-23 William Y. C. Chen , Qing-Hu Hou , Yan-Ping Mu

A new strategy for the reconstruction of $f(R)$ gravity models have been attempted using Raychaudhuri equation. Two examples, one for an eternally accelerating universe and the other for one that mimics a ${\Lambda}$CDM expansion history…

General Relativity and Quantum Cosmology · Physics 2019-04-09 Shibendu Gupta Choudhury , Ananda Dasgupta , Narayan Banerjee

Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…

q-alg · Mathematics 2008-02-03 Katrina D. Barron

The semisimple part of d-dimensional Galilean conformal algebra g^(d) is given by h^(d)=O(2,1)+O(d), which after adding via semidirect sum the 3d-dimensional Abelian algebra t^(d) of translations, Galilean boosts and constant accelerations…

Mathematical Physics · Physics 2011-09-29 Sergey Fedoruk , Jerzy Lukierski

In this paper, based a novel primal-dual dynamical model with adaptive scaling parameters and Bregman divergences, we propose new accelerated primal-dual proximal gradient splitting methods for solving bilinear saddle-point problems with…

Optimization and Control · Mathematics 2024-09-04 Hao Luo

We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2\phi_1$…

Quantum Algebra · Mathematics 2007-05-23 T. H. Baker , P. J. Forrester