Related papers: Holonomic Tools for Basic Hypergeometric Functions
In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems. The main purpose of this paper is to…
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
The purpose of this paper is to introduce and study a q-analogue of the holonomic system of differential equations associated to the Belavin's classical r-matrix (elliptic r-matrix equations), or, equivalently, to define an elliptic…
A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was…
We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that depend on a symbolic parameter.…
In this paper, we present a $q$-analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the $q$-Gosper representation, we describe the structure of rational functions that are summable when…
This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…
We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of…
In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly to topological data analysis. The…
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…
We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
We present some elementary derivations of summation and transformation formulas for q-series, which are different from, and in several cases simpler or shorter than, those presented in the Gasper and Bahman [1990] "Basic Hypergeometric…
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric…
This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The aim of this paper is to give mathematical foundations to Holonomic Quantum Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos…