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Gaudin's model and the generating function of the Wroński map

Inna Scherbak (2003)

Banach Center Publications

We consider the Gaudin model associated to a point z ∈ ℂⁿ with pairwise distinct coordinates and to the subspace of singular vectors of a given weight in the tensor product of irreducible finite-dimensional sl₂-representations, [G]. The Bethe equations of this model provide the critical point system of a remarkable rational symmetric function. Any critical orbit determines a common eigenvector of the Gaudin hamiltonians called a Bethe vector. In [ReV], it was shown that for generic...

Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto (2003)

Annales de l’institut Fourier

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

Generalization of the Modified Bessel Function and Its Generating Function

Griffiths, J., Leonenko, G., Williams, J. (2005)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25This paper presents new generalizations of the modified Bessel function and its generating function. This function has important application in the transient solution of a queueing system.

Generalizations of Milne’s U ( n + 1 ) q -Chu-Vandermonde summation

Jian-Ping Fang (2016)

Czechoslovak Mathematical Journal

We derive two identities for multiple basic hyper-geometric series associated with the unitary U ( n + 1 ) group. In order to get the two identities, we first present two known q -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two U ( n + 1 ) q -Chu-Vandermonde summations established by Milne, we arrive at our...

Generalized Cesàro operators on certain function spaces

Sunanda Naik (2010)

Annales Polonici Mathematici

Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators b , c is bounded on the Dirichlet spaces p , a . We also give a short and direct proof of boundedness of b , c on the Hardy space H p for 1 < p < ∞.

Generalized Krawtchouk polynomials: New properties

Norris Sookoo (2000)

Archivum Mathematicum

Orthogonality conditions and recurrence relations are presented for generalized Krawtchouk polynomials. Coefficients are evaluated for the expansion of an arbitrary polynomial in terms of these polynomials and certain special values for generalized Krawtchouk polynomials are obtained. Summations of some of these polynomials and of certain products are also considered.

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