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Register a new userGenerating functions for the Bannai-Ito polynomials
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The generating function of the Bannai-Ito polynomials is derived using the fact that these polynomials are known to be essentially the Racah or $6j$ coefficients of the $mathfrak{osp}(1|2)$ Lie superalgebra. The derivation is carried in a realization of the recoupling problem in terms of three Dunkl oscillators.
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This paper introduces and studies the Heun-Racah and Heun-Bannai-Ito algebras abstractly and establishes the relation between these new algebraic structures and generalized Heun-type operators derived from the notion of algebraic Heun operators in the case of the Racah and Bannai-Ito algebras.
Symbolic methods of umbral nature play an important and increasing role in the theory of special functions and in related fields like combinatorics. We discuss an application of these methods to the theory of lacunary generating functions for the Laguerre polynomials for which we give a number of new closed form expressions. We present furthermore the different possibilities offered by the method we have developed, with particular emphasis on their link to a new family of special functions and with previous formulations, associated with the theory of quasi monomials.
We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions of certain classes of Laguerre polynomials.
Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generating functions are obtained using two different approaches respectively based on the coherent-state representation and the position representation of osp(1j2).
We present a simple formula for the generating function for the polynomials in the $d$--dimensional semiclassical wave packets. We then use this formula to prove the associated Rodrigues formula.
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