19,483 research outputs found
Identities of nonterminating series by Zeilberger's algorithm
This paper argues that automated proofs of identities for non-terminating
hypergeometric series are feasible by a combination of Zeilberger's algorithm
and asymptotic estimates. For two analogues of Saalsch\"utz' summation formula
in the non-terminating case this is illustrated.Comment: 12 page
Special functions and q-commuting variables
This paper is mostly a survey, with a few new results. The first part deals
with functional equations for q-exponentials, q-binomials and q-logarithms in
q-commuting variables and more generally under q-Heisenberg relations. The
second part discusses translation invariance of Jackson integrals, q-Fourier
transforms and the braided line.Comment: plain TeX, 35 pages; Univ. of Amsterdam, Dept. of Math.; to appear in
"Special Functions, q-Series and Related Topics", The Fields Institute
Communications Series, minor revision, mainly linguisti
Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators
For each of the eight -th derivative parameter changing formulas for Gauss
hypergeometric functions a corresponding fractional integration formula is
given. For both types of formulas the differential or integral operator is
intertwining between two actions of the hypergeometric differential operator
(for two sets of parameters): a so-called transmutation property. This leads to
eight fractional integration formulas and four generalized Stieltjes transform
formulas for each of the six different explicit solutions of the hypergeometric
differential equation, by letting the transforms act on the solutions. By
specialization two Euler type integral representations for each of the six
solutions are obtained
Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation
This paper gives some further details of proofs of some theorems related to
the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in
"Lectures on the dynamical Yang-Baxter equation" by P. Etingof and O.
Schiffmann, math.QA/9908064. This concerns the intertwining operator, the
fusion matrix, the exchange matrix and the difference operators. The last part
expands proofs given in "Traces of intertwiners for quantum groups and
difference equations, I" by P. Etingof and A. Varchenko, math.QA/9907181. This
concerns the dual Macdonald-Ruijsenaars equations. This paper does not claim
originality, priority or completeness. It is meant as a service to whoever may
take profit of it.Comment: 14 page
- …