Results 61 to 70 of about 1,508 (88)
On Schur parameters in Steklov's problem [PDF]
arXiv, 2016 We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.
arxiv
Avoiding maximal parabolic subgroups of S_k [PDF]
arXiv, 2000 We find an explicit expression for the generating function of the number of permutations in S_n avoiding a subgroup of S_k generated by all but one simple transpositions. The generating function turns out to be rational, and its denominator is a rook polynomial for a rectangular board.
arxiv
Divergent Cesaro and Riesz means of Jacobi and Laguerre expansions [PDF]
arXiv, 2002 We show that for $\delta$ below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesaro and Riesz means of order $\delta$.
arxiv
Quasimodular solutions of a differential equation of hypergeometric type [PDF]
arXiv, 2002 Solutions which are quasimodular forms to a second order differential equation attached to a triangular group are explicitly described in terms of certain orthogonal polynomials.
arxiv
New bounds on the Hermite polynomials [PDF]
arXiv, 2004 We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of $|H_k(x)| e^{-x^2/2},$ on the real axis, where $H_k$ are the Hermite polynomials.
arxiv
Alternative Orthogonal Polynomials [PDF]
arXiv, 2004 The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of the inverse orthogonalization procedure.
arxiv
Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite [PDF]
arXiv, 2005 We analyze the Hermite polynomials $H_{n}(\xi)$ and their zeros asymptotically as $n\to\infty,$ using the limit relation between the Charlier and Hermite polynomials. Our formulas involve some special functions and they yield very accurate approximations.
arxiv
Parameter-based Fisher's information of orthogonal polynomials [PDF]
arXiv, 2006 The Fisher information of the classical orthogonal polynomials with respect to a parameter is introduced, its interest justified and its explicit expression for the Jacobi, Laguerre, Gegenbauer and Grosjean polynomials found.
arxiv
The $M_{L}(z);C_{L}(z);W_{L}(z)$ associated Laguerre Polynomials [PDF]
arXiv, 2000 In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .
arxiv
Topics on Meixner families [PDF]
arXiv, 2008 We shed the light on the inter-connections between different characterizations leading to the classical, free and quantum Meixner families.
arxiv