Resummation at finite conformal spin by Carlos Cardona, Sunny Guha, Surya Kiran Kanumilli, Kallol Sen

“…By using the inversion formula of Caron-Huot and the integral (Mellin) representation of conformal blocks, we show that the contribution from individual exchanges to anomalous dimensions and corrections to the OPE coefficients for “double-twist” operators O 1 O 2 Δ , J $$ {\left[{\mathcal{O}}_1{\mathcal{O}}_2\right]}_{\Delta, J} $$ in s-channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic with respect to space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.…”
Get full text

Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials by Ernest G. Kalnins, Willard Miller Jr., Sarah Post

“…By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. …”
Get full text

A Relativistic Conical Function and its Whittaker Limits by Simon Ruijsenaars

“…In previous work we introduced and studied a function R(a+,a−,c;v,vˆ) that is a generalization of the hypergeometric function _2F_1 and the Askey-Wilson polynomials. When the coupling vector c∈C^4 is specialized to (b,0,0,0), b∈C, we obtain a function R(a+,a−,b;v,2vˆ) that generalizes the conical function specialization of _2F_1 and the q-Gegenbauer polynomials. …”
Get full text

The Quantum Superalgebra osp[subscript q] (1|2) and a q-Generalization of the Bannai–Ito Polynomials by Vinet, Luc, Zhedanov, Alexei, Genest, Vincent

“…The relation between these q-deformed Bannai–Ito polynomials and the q-Racah/Askey–Wilson polynomials is discussed.…”
Get full text

Formulae for Askey-Wilson moments and enumeration of staircase tableaux by Corteel, S., Stanton, D., Williams, L., Stanley, Richard P

“…We explain how the moments of the (weight function of the) Askey-Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. …”
Get full text
Get full text

Anomalous dimensions from crossing kernels by Charlotte Sleight, Massimo Taronna

“…To this end, we underline a connection between: Wilson polynomials (which naturally appear when considering the crossing kernels given recently in arXiv:1804.09334 ), the spectral integral in the conformal partial wave expansion, and Wilson functions. …”
Get full text

Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz by Pascal Baseilhac, Rodrigo A. Pimenta

“…For a special case, the Q-polynomial is identified with the Askey-Wilson polynomial, which allows one to obtain the solution of the associated Bethe ansatz equations. …”
Get full text