Classification of polynomial solutions of second-order difference equation of hypergeometric type with real coefficients, orthogonal with respect to a positive symmetric weight function is presented.
Let fP n (x)g 1 n=0 and fQ m (x)g 1 m=0 be two families of orthogonal polynomials. The linearization problem involves only one family via the relation: P i (x) P j (x) = i+j X k=ji?jj L ijk P k (x) and the connection problem mixes both families: P n (x) = n X m=0 C m (n) Q m (x): In many cases, it is possible to build a recurrence relation involving only m… (More)
—The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the probability distributions because it is controlled by the (local) Fisher information, which is a gradient functional of the… (More)
Three different methods, namely maximum en-tropy, combination of Dirac deltas and two-point Padé ap-proximants, are used to construct tight model-independent approximations to the atomic form factor F(k) in terms of a few quantities related to its inverse Fourier trnsform, i.e. the one-particle density ρ(r). The accuracy of these approximations is analyzed… (More)
The asymptotic contracted measure of zeros of a large class of orthogonal polynomials is explicitly given in the form of a Lauricella function. The polynomials are defined by means of a three-term recurrence relation whose coefficients may be unbounded but vary regularly and have a different behaviour for even and odd indices. Subclasses of systems of… (More)
Three different mathematical techniques (maximum-entropy, Stieltjes-type and Pad&like approximants) are used to obtain tight approximations to scattering intensities in terms of a few local and/or global quantities related to the electron-pair density. The accuracy of the approximations is analyzed and compared by means of Hylleraas-type atomic… (More)