34 citations · 312 across the 53 of their papers we have counts for
8 papers · 1 filter
An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)
Hjalmar Rosengren
Elliptic 6j-symbols first appeared in connection with solvable models of statistical mechanics. They include many interesting limit cases, such as quantum 6j-symbols (or q-Racah po…
On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
Hjalmar Rosengren, Michael Schlosser
Using Krattenthaler's operator method, we give a new proof of Warnaar's recent elliptic extension of Krattenthaler's matrix inversion. Further, using a theta function identity clos…
New transformations for elliptic hypergeometric series on the root system An
Hjalmar Rosengren
Recently, Kajihara gave a Bailey-type transformation relating basic hypergeometric series on the root system An, with different dimensions n. We give, with a new, elementary, proof…
On a hypergeometric identity of Gelfand, Graev and Retakh
Christian Krattenthaler, Hjalmar Rosengren
A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of different…
Elliptic U(2) quantum group and elliptic hypergeometric series
Erik Koelink, Yvette van Norden, Hjalmar Rosengren
We investigate an elliptic quantum group introduced by Felder and Varchenko, which is constructed from the -matrix of the Andrews-Baxter-Forrester model, containing both spectra…
Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
Hjalmar Rosengren, Michael Schlosser
Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new…
Continuous Hahn functions as Clebsch-Gordan coefficients
Wolter Groenevelt, Erik Koelink, Hjalmar Rosengren
An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-p…
A bilateral series involving basic hypergeometric functions
Hjalmar Rosengren
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements o…