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118
On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
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Cited by 38 (1 self)
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We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
Scaling limit for the spacetime covariance of the stationary totally asymmetric simple exclusion process
 Comm. Math. Phys
"... The totally asymmetric simple exclusion process (TASEP) on the onedimensional lattice with the Bernoulli ρ measure as initial conditions, 0 < ρ < 1, is stationary in space and time. Let Nt(j) be the number of particles which have crossed the bond from j to j + 1 during the time span [0,t]. For j = ..."
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Cited by 37 (9 self)
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The totally asymmetric simple exclusion process (TASEP) on the onedimensional lattice with the Bernoulli ρ measure as initial conditions, 0 < ρ < 1, is stationary in space and time. Let Nt(j) be the number of particles which have crossed the bond from j to j + 1 during the time span [0,t]. For j = (1 − 2ρ)t + 2w(ρ(1 − ρ)) 1/3 t 2/3 we prove that the fluctuations of Nt(j) for large t are of order t 1/3 and we determine the limiting distribution function Fw(s), which is a generalization of the GUE TracyWidom distribution. The family Fw(s) of distribution functions have been obtained before by Baik and Rains in the context of the PNG model with boundary sources, which requires the asymptotics of a RiemannHilbert problem. In our work we arrive at Fw(s) through the asymptotics of a Fredholm determinant. Fw(s) is simply related to the scaling function for the spacetime covariance of the stationary TASEP, equivalently to the asymptotic transition
Representations of Orthogonal Polynomials
, 1998
"... Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions of this algorithm all ..."
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Cited by 26 (9 self)
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Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions of this algorithm allow the computation of recurrence and differential equations from Rodrigues type formulas and from generating functions. In particular, these algorithms can be used to compute the differential/difference and recurrence equations for the classical continuous and discrete orthogonal polynomials from their hypergeometric representations, and from their Rodrigues representations and generating functions. In recent work, we used an explicit formula for the recurrence equation of families of classical continuous and discrete orthogonal polynomials, in terms of the coefficients of their differential/difference equations, to give an algorithm to identify the polynomial system from a given recurrence equation....
A Logarithmically Completely monotonic Function Involving the Gamma Functions 1
"... We show that the function x → [Γ(x+1)]1/x x[Γ(x+2)] 1/(x+1) is logarithmically completely monotonic on (0, ∞). This answers a question by A.Vernescu. ..."
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Cited by 16 (12 self)
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We show that the function x → [Γ(x+1)]1/x x[Γ(x+2)] 1/(x+1) is logarithmically completely monotonic on (0, ∞). This answers a question by A.Vernescu.
On ZoneBalancing of PeertoPeer Networks: Analysis of Random Node Join
, 2004
"... Balancing peertopeer graphs, including zonesize distributions, has recently become an important topic of peertopeer (P2P) research [1], [2], [6], [19], [31], [36]. To bring analytical understanding into the various peerjoin mechanisms, we study how zonebalancing decisions made during the initi ..."
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Cited by 11 (4 self)
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Balancing peertopeer graphs, including zonesize distributions, has recently become an important topic of peertopeer (P2P) research [1], [2], [6], [19], [31], [36]. To bring analytical understanding into the various peerjoin mechanisms, we study how zonebalancing decisions made during the initial sampling of the peer space a#ect the resulting zone sizes and derive several asymptotic results for the maximum and minimum zone sizes that hold with high probability.
Polygamma functions of negative order
 J. Comp. and Appl. Math
, 1998
"... Liouville's fractional integration is used to de ne polygamma functions (n) (z) for negative integern. It's shown that such (n) (z) can be represented in a closed form by means of the rst derivatives of the Hurwitz Zeta function. Relations to the Barnes Gfunction and generalized Glaisher's constan ..."
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Cited by 10 (3 self)
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Liouville's fractional integration is used to de ne polygamma functions (n) (z) for negative integern. It's shown that such (n) (z) can be represented in a closed form by means of the rst derivatives of the Hurwitz Zeta function. Relations to the Barnes Gfunction and generalized Glaisher's constants are also discussed. 1
Analytical And Numerical Studies Of The Convergence Behavior Of The J Transformation
 of the J transformation, J. Comput. Appl. Math
, 1996
"... A new nonlinear sequence transformation, the iterative J transformation, was proposed recently [H. H. H. Homeier, Some applications of nonlinear convergence accelerators, Int. J. Quantum Chem. 45, 545  562 (1993)]. For this transformation, a derivation based on the method of hierarchical consisten ..."
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Cited by 9 (9 self)
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A new nonlinear sequence transformation, the iterative J transformation, was proposed recently [H. H. H. Homeier, Some applications of nonlinear convergence accelerators, Int. J. Quantum Chem. 45, 545  562 (1993)]. For this transformation, a derivation based on the method of hierarchical consistency, alternative recursive representations, general properties, an explicit expression for the kernel, model sequences, and its relation to other sequence transformations have been given [H. H. H. Homeier, A hierarchically consistent, iterative sequence transformation, Numer. Algo., in press]. The J transformation is of similar generality as the wellknown E algorithm [C. Brezinski, A general extrapolation algorithm, Numer. Math. 35, 175  180 (1980). T. Havie, Generalized Neville type extrapolation schemes, BIT 19, 204  213 (1979)]. In the present contribution, some results on convergence acceleration properties of the J transformation are proved. Numerical test results are presented which ...
Algorithms for Classical Orthogonal Polynomials
, 1996
"... In this article explicit formulas for the recurrence equation pn+1 (x) = (An x +Bn ) pn (x) \Gamma Cn pn\Gamma1 (x) and the derivative rules oe(x) p 0 n (x) = ff n pn+1 (x) + fi n pn (x) + fl n pn\Gamma1 (x) and oe(x) p 0 n (x) = (~ff n x + ~ fi n ) pn (x) + ~ fl n pn\Gamma1 (x) respectively ..."
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Cited by 7 (4 self)
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In this article explicit formulas for the recurrence equation pn+1 (x) = (An x +Bn ) pn (x) \Gamma Cn pn\Gamma1 (x) and the derivative rules oe(x) p 0 n (x) = ff n pn+1 (x) + fi n pn (x) + fl n pn\Gamma1 (x) and oe(x) p 0 n (x) = (~ff n x + ~ fi n ) pn (x) + ~ fl n pn\Gamma1 (x) respectively which are valid for the orthogonal polynomial solutions pn (x) of the differential equation oe(x) y 00 (x) + (x) y 0 (x) + n y(x) = 0 of hypergeometric type are developed that depend only on the coefficients oe(x) and (x) which themselves are polynomials w.r.t. x of degrees not larger than 2 and 1, respectively. Partial solutions of this problem had been previously published by Tricomi, and recently by Y'a~nez, Dehesa and Nikiforov. Our formulas yield an algorithm with which it can be decided whether a given holonomic recurrence equation (i.e. one with polynomial coefficients) generates a family of classical orthogonal polynomials, and returns the corresponding data (density function,...
Scalar Levintype sequence transformations
 81–147 of Brezinski, C. (Editor), Numerical
, 2000
"... Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. The basic idea is to construct from a given sequence {sn} a new sequence {s ′ n} = T ( {sn}) where each s ′ n depends on a finite n ..."
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Cited by 7 (1 self)
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Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. The basic idea is to construct from a given sequence {sn} a new sequence {s ′ n} = T ( {sn}) where each s ′ n depends on a finite number of elements sn1,..., snm. Often, the sn are the partial sums of an infinite series. The aim is to find transformations such that {s ′ n} converges faster than (or sums) {sn}. Transformations T ( {sn}, {ωn}) that depend not only on the sequence elements or partial sums sn but also on an auxiliary sequence of socalled remainder estimates ωn are of Levintype if they are linear in the sn, and nonlinear in the ωn. Such remainder estimates provide an easytouse possibility to use asymptotic information on the problem sequence for the construction of highly efficient sequence transformations. As shown first by Levin, it is possible to obtain such asymptotic information easily for large classes of sequences in such a way that the ωn are simple functions of a few sequence elements sn. Then, nonlinear sequence transformations are obtained. Special cases of such Levintype
Bifurcations of periodic orbits and uniform approximations
 J. Phys. AMath. Gen
, 1997
"... We derive uniform approximations for contributions to Gutzwiller’s periodicorbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contribu ..."
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Cited by 7 (2 self)
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We derive uniform approximations for contributions to Gutzwiller’s periodicorbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller’s type would diverge at the bifurcation. New results for the tangent, the period doubling and the period tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results. PACS numbers: 03.20.+i Classical mechanics of discrete systems: general mathematical aspects. 03.65.Sq Semiclassical theories and applications. 05.45.+b Theory and models of chaotic systems. Submitted to Journal of Physics A 1 1