ML p(r)ior | Holonomic Tools for Basic Hypergeometric Functions

Holonomic Tools for Basic Hypergeometric Functions

2016-02-01
1602.00454 | cs.SC
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric functions. A major objective of this article is to popularize the usage of such tools also in these domains. Concrete case studies showing software in action introduce to the basic techniques. An application highlight is a new computer-assisted proof of the celebrated Ismail-Zhang formula, an important q-analog of a classical expansion formula of plane waves in terms of Gegenbauer polynomials.
PDF

Highlights - Most important sentences from the article

Login to like/save this paper, take notes and configure your recommendations

Related Articles

2019-03-25

We give an approximate formula of the distribution of the largest eigenvalue of real Wishart matrice… show more
PDF

Highlights - Most important sentences from the article

2019-04-16

For any complex parameters $x$ and $\nu$, we provide a new class of linear inversion formulas $T = A… show more
PDF

Highlights - Most important sentences from the article

2019-02-28
1902.11001 | math.CO

We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a s… show more
PDF

Highlights - Most important sentences from the article

2018-09-17

In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the e… show more
PDF

Highlights - Most important sentences from the article

2018-11-21
1811.08616 | cs.SC

A lot of information concerning solutions of linear differential equations can be computed directly … show more
PDF

Highlights - Most important sentences from the article

2014-07-10

A wide range of numerical methods exists for computing polynomial approximations of solutions of ord… show more
PDF

Highlights - Most important sentences from the article

2018-07-01
1807.03140 | math.NA

We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic… show more
PDF

Highlights - Most important sentences from the article

2012-03-19
1203.4200 | math.CO

We give necessary and sufficient conditions for the existence of telescopers for rational functions … show more
PDF

Highlights - Most important sentences from the article

2017-06-12

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, … show more
PDF

Highlights - Most important sentences from the article

2013-10-31
1310.8455 | cs.SC

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditi… show more
PDF

Highlights - Most important sentences from the article

2019-06-19
1906.07962 | math.NA

Sparse spectral methods for solving partial differential equations have been derived in recent years… show more
PDF

Highlights - Most important sentences from the article

2019-06-22

In this paper we describe a method for removing the numerical errors in the modeling of linear evolu… show more
PDF

Highlights - Most important sentences from the article

2019-07-15
1907.06394 | math.RA

We propose a functional description of rewriting systems on topological vector spaces. We introduce … show more
PDF

Highlights - Most important sentences from the article

2019-07-18

This work focuses on the study of partial differential equation (PDE) based basis function for Disco… show more
PDF

Highlights - Most important sentences from the article

2018-06-18

We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet a… show more
PDF

Highlights - Most important sentences from the article

2018-02-27
1802.09798 | math.CO

A Wilf--Zeilberger pair $(F, G)$ in the discrete case satisfies the equation $ F(n+1, k) - F(n, k) =… show more
PDF

Highlights - Most important sentences from the article

2015-07-17
1507.04840 | math.CO

In 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuo… show more