### 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.

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

# Related Articles

**2019-03-25**

1903.10099 | math.ST

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

**2019-04-16**

1904.08283 | math.CA

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

**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

**2018-09-17**

1809.06168 | cs.SC

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

**2018-11-21**

1811.08616 | cs.SC

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

**2014-07-10**

1407.2802 | cs.SC

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

**2018-07-01**

1807.03140 | math.NA

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

**2012-03-19**

1203.4200 | math.CO

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

**2017-06-12**

1706.03549 | cs.SY

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

**2013-10-31**

1310.8455 | cs.SC

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

**2019-06-19**

1906.07962 | math.NA

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

**2019-06-22**

1906.10743 | math.NA

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

**2019-07-15**

1907.06394 | math.RA

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

**2019-07-18**

1907.08309 | math.NA

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

**2018-06-18**

1806.06543 | math.NT

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

**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

**2015-07-17**

1507.04840 | math.CO

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