Further Generalization of Kobayashi's Gamma Function
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)
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...
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.
Some extensions of the properties of invariant polynomials proved by Davis (1980), Chikuse (1980), Chikuse and Davis (1986) and Ratnarajah et al. (2005) are given for symmetric and Hermitian matrices.
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.
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators is bounded on the Dirichlet spaces . We also give a short and direct proof of boundedness of on the Hardy space for 1 < p < ∞.