34 citations · 312 across the 53 of their papers we have counts for
22 papers · 1 filter
String theory amplitudes and partial fractions
Hjalmar Rosengren
We give rigorous proofs and generalizations of partial fraction expansions for string amplitudes that were recently discovered by Saha and Sinha.
Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
Hjalmar Rosengren, Michael J. Schlosser
Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we pres…
Determinantal elliptic Selberg integrals
Hjalmar Rosengren
The classical Selberg integral contains a power of the Vandermonde determinant. When that power is a square, it is easy to prove Selberg's identity by interpreting it as a determin…
Elliptic hypergeometric functions associated with root systems
Hjalmar Rosengren, S. Ole Warnaar
We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main eval…
Gustafson-Rakha-Type Elliptic Hypergeometric Series
Hjalmar Rosengren
We prove a multivariable elliptic extension of Jackson's summation formula conjectured by Spiridonov. The trigonometric limit case of this result is due to Gustafson and Rakha. As…
Rahman's biorthogonal functions and superconformal indices
Hjalmar Rosengren
We study biorthogonal functions related to basic hypergeometric integrals with coupled continuous and discrete components. Such integrals appear as superconformal indices for three…
Elliptic Hypergeometric Functions
Hjalmar Rosengren
In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehe…
Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices
Hjalmar Rosengren
We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for produ…
An elliptic determinant transformation
Hjalmar Rosengren
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series…
Elliptic determinant evaluations and the Macdonald identities for affine root systems
Hjalmar Rosengren, Michael Schlosser
We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polyno…
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…
Elliptic hypergeometric series on root systems
Hjalmar Rosengren
We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems A_n, C_n and D_n. In the special cases of classical and q-series,…
Karlsson-Minton type hypergeometric functions on the root system C_n
Hjalmar Rosengren
We prove a reduction formula for Karlsson-Minton type hypergeometric series on the root system C_n and derive some consequences of this identity. In particular, when combined with…
Reduction formulae for Karlsson-Minton type hypergeometric functions
Hjalmar Rosengren
We prove a master theorem for hypergeometric functions of Karlsson-Minton type, stating that a very general multilateral U(n) Karlsson-Minton type hypergeometric series may be redu…
A proof of a multivariable elliptic summation formula conjectured by Warnaar
Hjalmar Rosengren
We prove a multivariable elliptic analogue of Jackson's 8W7 summation formula, which was recently conjectured by S.O.Warnaar.
Transmutation kernels for the little q-Jacobi function transform
Erik Koelink, Hjalmar Rosengren
The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel…