In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde matrix VR(x) = [rj−1(xi)] with polynomials {rk(x)} related to a Hessenberg quasiseparable matrix. The result generalizes the well-known Björck-Pereyra algorithm for classical Vandermonde systems involving monomials. It also generalizes the algorithms of [RO91] for VR...

We give a recursion for the multivariate Rogers-Szegö polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all q-multinomial coefficients of some fixed degree and length, and give a recursion for this sum which follows from the recursion of the multivariate Rogers-Szegö polynomials, and generalizes the recursion for...

A variety of results in complex geometry and mathematical physics depend upon the analysis of holomorphic sections of high powers L⊗N of holomorphic line bundles L → M over compact Kähler manifolds ([A][Bis][Bis.V] [Bou.1][Bou.2][B.G][D][Don] [G][G.S][K][Ji] [T] [W]). The principal tools have been Hörmander’s L-estimate on the ∂̄-operator over M [T], the asymptotics of heat kernels kN (t, x, y) ...

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) normalized holomorphic bi-univalent functions in open unit disk U, which are associated with Bazilevič λ-pseudo-starlike as well Horadam polynomials. We estimate second third coefficients Taylor-Maclaurin expansions belonging to function class, here. Furthermore, esta...

The object of this paper is the relation between the Szegö kernel of an ample line bundle on a complex projective manifold, M , and the Szegö kernel of the induced polarization on the quotient of M by the holomorphic action of a compact Lie group, G. Let M be an n-dimensional complex projective manifold and L an ample line bundle on it. Suppose a connected compact Lie group G acts on M as a gro...