34 citations · 312 across the 53 of their papers we have counts for
7 papers · 2 filters
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…
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…