Gaussian hypergeometric series and supercongruences (2009)
Robert Osburn, Carsten Schneider
Abstract. Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to...
A Symbolic Summation Approach to Find Optimal Nested Sum Representations (2009)
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem...
A Refined Difference Field Theory for Symbolic Summation (2008)
In this article we present a refined summation theory based on Karr's difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the...
Parameterized Telescoping Proves Algebraic Independence of Sums (2008)
Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized...
Formal Power Series and Algebraic Combinatorics (2008)
Parameterized telescoping proves algebraic independence of sums
Automated Proofs for Some Stirling Number Identities (2008)
Manuel Kauers, Carsten Schneider
We present computer-generated proofs for some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number...
Peter Paule, Carsten Schneider
Taking an example from statistics, we show how symbolic summation can be used to find generalizations of binomial identities that involve infinite series. In such generalizations, the infinite series...
AUTOMATED PROOFS FOR SOME STIRLING NUMBER IDENTITIES (2008)
Manuel Kauers, Carsten Schneider
Abstract. We present computer-generated proofs of some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number...
Bierenbaum, Isabella, Blümlein, Johannes, Klein, Sebastian, Schneider, Carsten
We calculate the $O(\alpha_s^2)$ massive operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in...
Gaussian hypergeometric series and supercongruences (2008)
Robert Osburn, Carsten Schneider
Abstract. Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to...
To appear in Journal of Algebra and Its Applications SIMPLIFYING SUMS IN ΠΣ ∗-EXTENSIONS (2008)
We present telescoping algorithms which compute optimal sum representations of indefinite nested sums. More precisely, given a rational summand expression in terms of nested sums and products, the...
Apéry’s Double Sum is Plain Sailing Indeed (2008)
We demonstrate that also the second sum involved in Apéry’s proof of the irrationality of ζ(3) becomes trivial by symbolic summation. In his beautiful survey [4], van der Poorten explained that...
Abstract Indefinite Summation with Unspecified Summands (2008)
Manuel Kauers, Carsten Schneider
We provide a new algorithm for indefinite nested summation which is applicable to summands involving unspecified sequences x(n). More than that, we show how to extend Karr’s algorithm to a general...
Carsten Schneider, Johannes Kepler, Carsten Schneider
,,Doktor der technischen Wissenschaften“
Abstract Computer Proofs of a New Family of Harmonic Number Identities (2008)
Peter Paule, Carsten Schneider
In this paper we consider five conjectured harmonic number identities similar to those arising in the context of supercongruences for Apéry numbers. The general object of this article is to discuss...
Abstract. We present symbolic summation tools in the context of difference fields that help scientists in practical problem solving. Throughout this article we present multi-sum examples which are...
Peter Paule, Carsten Schneider
Taking an example from statistics, we show how symbolic summation can be used to find generalizations of binomial identities that involve infinite series. In such generalizations, the infinite series...
Abstract. We present symbolic summation tools in the context of difference fields that help scientists in practical problem solving. Throughout this article we present multi-sum examples which are...
Abstract Computer Proofs of a New Family of Harmonic Number Identities (2008)
Peter Paule, Carsten Schneider
In this paper we consider five conjectured harmonic number identities similar to those arising in the context of supercongruences for Apéry numbers. The general object of this article is to discuss...
Tako-Tsubo cardiomyopathy characteristics in long-term follow-up (2008)
Schneider, Carsten, Krause, Korff, Hertting, Klaus, Boczor, Sigrid, Wollner, Thomas, ...
Tako-Tsubo Cardiomyopathy (TTC) is described as left ventricular (LV) dysfunction with the phenomenon of "apical ballooning", rapidly resolving, without coronary artery stenoses.
Schneider, Carsten, Malisius, Rainer, Krause, Korff, Lampe, Friedrun, Bahlmann, Edda, Boczor, Sigrid, ...
Aims The aim of the study was to investigate the atrial myocardial deformation properties using ultrasound strain rate (SR) imaging in patients after catheter ablation of atrial fibrillation (AF) and...
Gerhard Arminger, Carsten Schneider
The forecasting of time series in goods management systems causes various problems that we identify and indicate possible solutions. The implementation of auxiliary information like promotional...
A Student Dictionary System (2007)
Fabrizio Caruso, Carsten Schneider
In this paper we present a detailed case study of formal systems specication with the aid of the term rewriting system cafeOBJ. The software system we use for this case study is a rather...
Schneider, Carsten, Jaquet, Kai, Malisius, Rainer, Geidel, Stephan, Bahlmann, Edda, Boczor, Sigrid, ...
Aims The aim of this study was to investigate whether erythropoietin (EPO) has cardioprotective effects in a chronic myocardial ischaemia model regarding strain-rate imaging parameters during...
When is 0.999... equal to 1 (2007)
Robin Pemantle, Carsten Schneider
The three dots in the title do not refer to an infinite sequence of 9’s, but to digits that are increasingly hard to compute. The question is philosophical: how many 9’s do we need to see before...
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...
A refined difference field theory for symbolic summation (2007)
In this article we present a refined summation theory based on Karr’s difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the...
Automated Proofs for Some Stirling Number Identities (2007)
Manuel Kauers, Carsten Schneider
We present computer-generated proofs for some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number...
When is 0.999... equal to 1 (2007)
Robin Pemantle, Carsten Schneider
The three dots in the title do not refer to an infinite sequence of 9’s, but to digits that are increasingly hard to compute. The question is philosophical: how many 9’s do we need to see before...
A refined difference field theory for symbolic summation, SFB-Report 2007-24 (2007)
In this article we present a refined summation theory based on Karr’s difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the...
How One Can Play with Sums Presented at the 8th Rhine Workshop on Computer Algebra ∗ (2007)
There are implementations of the celebrated Gosper algorithm (1978) and Zeilberger algorithm (1991) on almost any computer algebra platform. Inspired by Karr’s indefinite summation algorithm (1981)...
Parameterized telescoping proves algebraic independence of sums (2007)
Abstract. Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a...
Symbolic summation finds optimal nested sum representations (2007)
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain symbolic summation algorithms that solve this problem for...
Automated Proofs for Some Stirling Number Identities (2007)
Manuel Kauers, Carsten Schneider
We present computer-generated proofs for some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number...
When is 0.999... equal to 1 (2007)
Robin Pemantle, Carsten Schneider
Abstract. A doubly infinite sum, numerically evaluated at between 0.999 and 1.001, turns out to have a nice value. 1.
Symbolic summation assists combinatorics (2007)
Abstract. We present symbolic summation tools in the context of difference fields that help scientists in practical problem solving. Throughout this article we present multi-sum examples which are...
A refined difference field theory for symbolic summation, SFB-Report 2007-24 (2007)
In this article we present a refined summation theory based on Karr’s difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the...
Truncating Binomial Series with Symbolic Summation (2007)
Peter Paule, Carsten Schneider
Abstract. Taking an example from statistics, we show how symbolic summation can be used to find generalizations of binomial identities which involve infinite series. In such generalizations the...
Schneider, Carsten, Jaquet, Kai, Malisius, Rainer, Geidel, Stephan, Bahlmann, Edda, Boczor, Sigrid, ...
Aims The aim of this study was to investigate whether erythropoietin (EPO) has cardioprotective effects in a chronic myocardial ischaemia model regarding strain-rate imaging parameters during...
Gaussian hypergeometric series and supercongruences (2006)
Osburn, Robert, Schneider, Carsten
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number...
Indefinite summation with unspecified summands (2006)
Manuel Kauers, Carsten Schneider
We provide a new algorithm for indefinite nested summation which is applicable to summands involving unspecified sequences x(n). More than that, we show how to extend Karr’s algorithm to a general...
Some Notes On ``When is 0.999... equal to 1? (2006)
In joint work Robin Pemantle and I (2004) consider a doubly infinite sum which is not equal to 1, as first suspected, but evaluates to a sum of products of values of the zeta function. Subsequently,...
Schneider, Carsten, Ernst, Sabine, Bahlmann, Edda, Malisius, Rainer, Krumsdorf, Ulrike, Boczor, Sigrid, ...
Aims Pulmonary vein (PV) stenosis has been described as a complication after catheter ablation of atrial fibrillation. The aim of the study was to investigate the diagnostic role of transesophageal...
Some notes on “When is 0.999... equal to 1 (2005)
Carsten Schneider, C. Schneider
Abstract. In joint work Robin Pemantle and I (2004) consider a doubly infinite sum which is not equal to 1, as first suspected, but evaluates to a sum of products of values of the zeta function....
A new Sigma approach to multi-summation (2005)
Abstract. We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr 1981),...
Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation (2005)
Kathy Driver, Helmut Prodinger, Carsten Schneider
Abstract. Combinatorial identities that were needed in [24] are proved, mostly with C. Schneider’s computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary...
Product representations in ΠΣ-fields (2005)
Abstract. ΠΣ-fields are a very general class of difference fields that enable one to discover and prove multisum identities arising in combinatorics and special functions. In this article we focus...
A new Sigma approach to multi-summation (2005)
Abstract. We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr 1981),...
Generalized reciprocity laws for sums of harmonic numbers (2005)
Markus Kuba, Helmut Prodinger, Carsten Schneider
Abstract. We present summation identities for generalized harmonic numbers, which generalize reciprocity laws discovered when studying the algorithm quickselect. Furthermore, we demonstrate how the...
Product representations in ΠΣ-fields (2005)
Abstract. ΠΣ-fields are a very general class of difference fields that enable one to discover and prove multisum identities arising in combinatorics and special functions. In this article we focus...
Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation (2005)
Kathy Driver, Helmut Prodinger, Carsten Schneider
Abstract. Combinatorial identities that were needed in [24] are proved, mostly with C. Schneider’s computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary...
Generalized reciprocity laws for sums of harmonic numbers (2005)
Markus Kuba, Helmut Prodinger, Carsten Schneider
Abstract. We present summation identities for generalized harmonic numbers, which generalize reciprocity laws discovered when studying the algorithm quickselect. Furthermore, we demonstrate how the...
Der Universalmischer Speed-UNGUATOR-e-Dental der Firma CTW AG soll den Anmischvorgang von Materialien der zahnärztlichen Praxis erleichtern und neben dem verkürzten Zeitaufwand zu einer...
The summation package Sigma: Underlying principles and a rhombus tiling application (2004)
Abstract. We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General...
Symbolic summation with single-nested sum extensions (2004)
Abstract. We present a streamlined and refined version of Karr’s summation algorithm. Karr’s original approach constructively decides the telescoping problem in ΠΣ-fields, a very general class...
Plane partitions VI: Stembridge’s TSPP Theorem — a detailed algorithmic proof (2004)
George E. Andrews, Peter Paule, Carsten Schneider
Abstract. We provide a new proof of Stembridge’s theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern...
Plane partitions VI: Stembridge’s TSPP Theorem — a detailed algorithmic proof (2004)
George E. Andrews, Peter Paule, Carsten Schneider
Abstract. We provide a new proof of Stembridge’s theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern...
Padé approximations to the logarithm III: Alternative methods and additional results (2004)
Kathy Driver, Helmut Prodinger, Carsten Schneider
Abstract. We use C. Schneider’s summation software Sigma and a method due to Andrews-Newton-Zeilberger to reprove results from [5] and [24] as well as to prove new related material. 1.
Padé approximations to the logarithm III: Alternative methods and additional results (2004)
Kathy Driver, Helmut Prodinger, Carsten Schneider, André Weideman
Abstract. We use C. Schneider’s summation software Sigma and a method due to Andrews-Newton-Zeilberger to reprove results from [22] and [5] as well as to prove new related material. 1.
Abstract. An important application of solving parameterized linear difference equations in ΠΣ-fields, a very general class of difference fields, is simplifying of multi-sum expressions and proving...
The summation package Sigma: Underlying principles and a rhombus tiling application (2004)
We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles...
The summation package Sigma: Underlying principles and a rhombus tiling application (2004)
We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles...
Plane partitions VI: Stembridge’s TSPP Theorem — a detailed algorithmic proof (2004)
George E. Andrews, Peter Paule, Carsten Schneider
Abstract. We provide a new proof of Stembridge’s theorem which validated the Totally Symmetric Plane Partitions (TSPP) Conjecture. The overall strategy of our proof follows the same general pattern...
Abstract. An important application of solving parameterized linear difference equations in ΠΣ-fields, a very general class of difference fields, is simplifying of multi-sum expressions and proving...
www.elsevier.com/locate/yaama A new Sigma approach to multi-summation (2004)
We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr, 1981), but also...
The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application (2004)
We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles...
Dateien im PDf-Format
Entwicklung und Evaluation eines MMI für funkgestützte Unfallwarnungen (2002)
Schneider, Carsten, Dahmen-Zimmer, Katharina, Kostka, Markus, Marberger, Claus, Zimmer, Alf
Proceeding vom 38. BDP-Kongress für Verkehrspsychologie Universität Regensburg 2002, Arbeitsgruppe 7: Verkehr und Information: Die Optimierung des Mobilitätssystems.
The described algorithms enable one to find all solutions of parameterized linear difference equations within ΠΣ-fields, a very general class of difference fields. These algorithms can be applied...
The original publication in AAECC is available at www.springerlink.com. Note that the proof of Lemma 7 has been corrected. Abstract An important application of solving parameterized linear difference...
Kostenoptimale Prognose von Lasten in der Energiewirtschaft / (2002)
Zugl.: Wuppertal, Universiẗat, Diss., 2002.
Zimmer, Alf, Lange, Klaus, Bäuml, Karl-Heinz, Scheuchenpflug, Rainer, Tucha, Oliver, Schnell, Harald, ...
An Implementation of Karr's Summation Algorithm in Mathematica (2000)
Implementations of the celebrated Gosper algorithm (1978) for indefinite summation are available on almost any computer algebra platform. We report here about an implementation of an algorithm by...
An implementation of Karr’s summation algorithm (2000)
Implementations of the celebrated Gosper algorithm (1978) for indefinite summation are available on almost any computer algebra platform. We report here about an implementation of an algorithm by...
An implementation of Karr’s summation algorithm (2000)
Implementations of the celebrated Gosper algorithm (1978) for indefinite summation are available on almost any computer algebra platform. We report here about an implementation of an algorithm by...
Münster (Westfalen), Universiẗat, Diss., 1999 (Nur beschränkt für den Austausch).
An Implementation of Karr's Summation Algorithm in Mathematica (1999)
There are implementations of the celebrated Gosper algorithm (1978) on almost any computer algebra platform. Within my PhD thesis work I implemented Karr's Summation Algorithm (1981) in the...
Carsten Schneider, Matthias Klapper, Thomas Wenzel
: In this paper we use 4 different time series models to forecast sales in a goods management system. We use a variety of forecast combining techniques and measure the forecast quality by applying...
Bochum, Univ., Diss., 1999.
Arminger, Gerhard, Schneider, Carsten
The forecasting of time series in goods management systems causes various problems that we identify and indicate possible solutions. The implementation of auxiliary information like promotional...
Klapper, Matthias, Schneider, Carsten, Wenzel, Thomas
In this paper we use 4 different time series models to forecast sales in a goods management system. We use a variety of forecast combining techniques and measure the forecast quality by applying...
Baryonische Observable und chirale Symmetrie im SU(3) Nambu-Jona-Lasinio-Modell / (1998)
Bochum, Universiẗat, Diss., 1998.
Mikrofiche-Ausg.: 2 Mikrofiches : 24x
Zugl.: Eberswalde, Fachhochsch., Diplomarbeit.
Strangeness in the Scalar Form Factor of the Nucleon (1995)
Kim, Hyun-Chul, Blotz, Andree, Schneider, Carsten, Goeke, Klaus
The scalar form factor of the nucleon and related physical quantities are investigated in the framework of the semibosonized SU(3) Nambu-Jona-Lasinio soliton model. We take into account the...
Mikroreprod. eines Ms. 66 Bl. : graph. Darst.
Heidelberg, Univ., Diss., 1993.
Carsten Schneider, Gerhard Arminger, Alexandra Schwarz
Cyclical structure, hierarchical analysis of variance, factor analysis, liberalized energy market,