Lindel\"of Representations and (Non-)Holonomic Sequences (2009)
Flajolet, Philippe, Gerhold, Stefan, Salvy, Bruno
Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindel\"of, which belong to an attractive but largely forgotten...
Asymptotic Estimates for Some Number Theoretic Power Series (2009)
We derive asymptotic bounds for the ordinary generating functions of several classical arithmetic functions, including the Moebius, Liouville, and von Mangoldt functions. The estimates result from...
The Shape of the Value Sets of Linear Recurrence Sequences (2009)
We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed...
Convergence Properties of Kemp's q-Binomial Distribution (2008)
Gerhold, Stefan, Zeiner, Martin
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established....
A computer proof of Turán’s inequality (2008)
Abstract. We show how Turán’s inequality Pn(x) 2 −Pn−1(x)Pn+1(x) ≥ 0 for Legendre polynomials and related inequalities can be proven by means of a computer procedure. The use of this...
Levy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing (2008)
Glasserman and Yu (Ann. Appl. Probab. 14, 2004, p. 2090) have investigated the mean square error in the Longstaff-Schwartz algorithm for American option pricing, assuming that the underlying process...
Point Lattices and Oscillating Recurrence Sequences (2008)
We consider the following question: Which real sequences (a(n)) that satisfy a linear recurrence with constant coefficients are positive for sufficiently large n? We show that the answer is negative...
A computer proof of Turán’s inequality (2008)
Abstract. We show how Turán’s inequality Pn(x) 2 −Pn−1(x)Pn+1(x) ≥ 0 for Legendre polynomials and related inequalities can be proven by means of a computer procedure. The use of this...
On the Non-Holonomic Character of Logarithms, Powers, and the Nth Prime Function (2008)
Philippe Flajolet Philippe, Stefan Gerhold, Bruno Salvy
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open...
Stefan Gerhold, Carsten Schneider, Lev Glebsky, Lomas A, Slp México, Howard Weiss, ...
The Schelling segregation models are “agent based ” population models, where individual members of the population (agents) interact directly with other agents and move in space and time. In this...
Non-Holonomicity of Sequences Defined via Elementary Functions (2006)
Bell, Jason P., Gerhold, Stefan, Klazar, Martin, Luca, Florian
We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences...
The Positivity Set of a Recurrence Sequence (2005)
Bell, Jason P., Gerhold, Stefan
We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case...
Point Lattices and Oscillating Recurrence Sequences (2005)
We consider the following question: Which real sequences (a(n)) that satisfy a linear recurrence with constant coefficients are positive for sufficiently large n? We show that the answer is negative...
On the non-holonomic character of logarithms, powers, and the n-th prime function (2005)
Flajolet, Philippe, Gerhold, Stefan, Salvy, Bruno
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of...
On the non-holonomic character of logarithms, powers, and the nth prime function (2005)
Philippe Flajolet, Stefan Gerhold, Bruno Salvy
Abstract. We establish that the sequences formed by logarithms and by “fractional ” powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open...
Combinatorial Sequences: Non-Holonomicity and Inequalities (2005)
Stefan Gerhold, Peter Paule, Peter Paule, ...
iv Holonomic functions (respectively sequences) satisfy linear ordinary differential equations (respectively recurrences) with polynomial coefficients. This class can be generalized to functions of...
The Positivity Set of a Recurrence Sequence (2005)
We consider real sequences (fn) that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where...
stefan.gerhold AT risc.uni-linz.ac.at (2005)
On the non-holonomic character of logarithms, powers,
A procedure for proving special function inequalities involving a discrete parameter (2005)
We define a class of special function inequalities that contains many classical examples, such as the Cauchy-Schwarz inequality, and introduce a proving procedure based on induction and Cylindrical...
On some non-holonomic sequences (2004)
A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with polynomial...
On some non-holonomic sequences (2004)
Abstract A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with...
On some non-holonomic sequences (2004)
A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with polynomial...
On some non-holonomic sequences (2004)
Abstract A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with...