Related papers: Holonomic Tools for Basic Hypergeometric Functions
Ismail and Wilson derived a generating function for Askey--Wilson polynomials which is given by a product of $q$-Gauss (Heine) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…
The main aim of this work is to derive the $q$-recurrence relations, $q$-partial derivative relations and summation formula of bibasic Humbert hypergeometric function $\Phi_1$ on two independent bases $q$ and $q_{1}$ of two variables and…
In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…
We show how the continuous Almkvist-Zeilberger algorithm can be used to efficiently discover and prove differential equations satisfied by generating functions of sequences defined as integrals of powers of C-finite polynomial sequences…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
By means of the $q$-Zeilberger algorithm, we prove a basic hypergeometric supercongruence modulo the fifth power of the cyclotomic polynomial $\Phi_n(q)$. This result appears to be quite unique, as in the existing literature so far no basic…
We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…
New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a…
I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the…
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of…