Symbolic Summation and Combinatorial Identities [SFB F1305-1]

Project Description

P.Paule.
Budget: 178.775,– Eur.

Project Lead

Project Duration

01/04/1998 - 31/03/2001

Project URL

Go to Website

Publications

2017

Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra

Peter Paule, Cristian-Silviu Radu

In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider and E. Zima. (ed.), pp. 1-41. 2017. Springer, 1019-7168 . [pdf]
[bib]
@incollection{RISC5475,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra}},
booktitle = {{Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday}},
language = {english},
pages = {1--41},
publisher = {Springer},
isbn_issn = {1019-7168 },
year = {2017},
editor = {C. Schneider and E. Zima.},
refereed = {yes},
length = {41}
}

2016

Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra

Manuel Kauers, Peter Paule, Greg Reid

ACM Communications in Computer Algebra 50(Issue 1), pp. 27-34. March 2016. 1932-2240. [pdf]
[bib]
@article{RISC5284,
author = {Manuel Kauers and Peter Paule and Greg Reid},
title = {{Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {Issue 1},
pages = {27--34},
isbn_issn = {1932-2240},
year = {2016},
month = {March},
refereed = {no},
length = {8}
}

A New Witness Identity for $11|p(11n+6)$

Peter Paule, Cristian-Silviu Radu

In: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, George E. Andrews, Frank Garvan (ed.), pp. 625-640. 2016. Springer, 2194-1009. [pdf]
[bib]
@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A New Witness Identity for $11|p(11n+6)$}},
booktitle = {{Analytic Number Theory, Modular Forms and q-Hypergeometric Series}},
language = {english},
pages = {625--640},
publisher = {Springer},
isbn_issn = { 2194-1009},
year = {2016},
editor = { George E. Andrews and Frank Garvan},
refereed = {yes},
length = {16}
}

2014

Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II

Christoph Koutschan, Peter Paule, Sergei K. Suslov

In: Algebraic and Algorithmic Aspects of Differential and Integral Operators, Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz (ed.), Lecture Notes in Computer Science 8372, pp. 135-145. 2014. Springer, Berlin Heidelberg, ISBN 978-3-642-54478-1. [pdf]
[bib]
@incollection{RISC4847,
author = {Christoph Koutschan and Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II}},
booktitle = {{Algebraic and Algorithmic Aspects of Differential and Integral Operators}},
language = {english},
abstract = {We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic closure properties in a sophisticated way.},
series = {Lecture Notes in Computer Science},
volume = {8372},
pages = {135--145},
publisher = {Springer},
address = {Berlin Heidelberg},
isbn_issn = {ISBN 978-3-642-54478-1},
year = {2014},
editor = {Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz},
refereed = {yes},
length = {11}
}

2013

Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.

Peter Paule, Sergei K. Suslov

In: Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013, Carsten Schneider, Johannes Blümlein (ed.), pp. 225-241. 2013. Springer, 978-3-7091-1615-9.
[bib]
@incollection{RISC4718,
author = {Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.}},
booktitle = {{Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013}},
language = {english},
pages = {225--241},
publisher = {Springer},
isbn_issn = {978-3-7091-1615-9},
year = {2013},
editor = {Carsten Schneider and Johannes Blümlein},
refereed = {no},
length = {17}
}

Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift

Peter Paule

1st edition, 2013. Springer, 978-3-319-00965-0.
[bib]
@booklet{RISC4850,
author = {Peter Paule},
title = {{Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift}},
language = {english},
publisher = {Springer},
isbn_issn = {978-3-319-00965-0},
year = {2013},
edition = {1st},
translation = {0},
length = {113}
}

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann

In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC]. [url]
[bib]
@incollection{RISC4721,
author = {S. Gerhold and M. Kauers and C. Koutschan and P. Paule and C. Schneider and B. Zimmermann},
title = {{Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order}},
booktitle = {{Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
pages = {75--96},
publisher = {Springer},
isbn_issn = {ISBN-13: 978-3709116159},
year = {2013},
note = {arXiv:1305.4818 [cs.SC]},
editor = {C. Schneider and J. Bluemlein},
refereed = {no},
length = {22},
url = {http://arxiv.org/abs/1305.4818}
}

2012

MacMahon's Dream

George E. Andrews and Peter Paule

In: Partitions, q-Series, and Modular Forms, K. Alladi and F. Garvan (ed.), Developments in Mathematics 23, pp. 1-12. 2012. Springer, 978-1-4614-0028-8.
[bib]
@incollection{RISC5157,
author = {George E. Andrews and Peter Paule},
title = {{MacMahon's Dream}},
booktitle = {{Partitions, q-Series, and Modular Forms}},
language = {english},
series = {Developments in Mathematics},
volume = {23},
pages = {1--12},
publisher = {Springer},
isbn_issn = {978-1-4614-0028-8},
year = {2012},
editor = {K. Alladi and F. Garvan},
refereed = {yes},
length = {12}
}

2011

The Concrete Tetrahedron

Manuel Kauers, Peter Paule

Text and Monographs in Symbolic Computation 1st edition, 2011. Springer Wien, 978-3-7091-0444-6.
[bib]
@book{RISC4162,
author = {Manuel Kauers and Peter Paule},
title = {{The Concrete Tetrahedron}},
language = {english},
series = {Text and Monographs in Symbolic Computation},
publisher = {Springer Wien},
isbn_issn = {978-3-7091-0444-6},
year = {2011},
edition = {1st},
translation = {0},
length = {210}
}

Automatic Improvements of Wallis' Inequality

P. Paule, V. Pillwein

In: SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida and others (ed.), pp. 12-16. 2011. IEEE Computer Society, 0. [pdf]
[bib]
@inproceedings{RISC4297,
author = {P. Paule and V. Pillwein},
title = {{Automatic Improvements of Wallis' Inequality}},
booktitle = {{SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing}},
language = {english},
pages = {12--16},
publisher = {IEEE Computer Society},
isbn_issn = {0},
year = {2011},
editor = {T.~Ida and others},
refereed = {no},
length = {5}
}

2010

Infinite Families of Strange Partition Congruences for Broken 2-Diamonds

Peter Paule, Silviu Radu

The Ramanujan Journal 23, pp. 409-416. 2010. ISSN 1382-4090. [pdf]
[bib]
@article{RISC4294,
author = {Peter Paule and Silviu Radu},
title = {{Infinite Families of Strange Partition Congruences for Broken 2-Diamonds }},
language = {english},
journal = {The Ramanujan Journal},
volume = {23},
pages = {409--416},
isbn_issn = {ISSN 1382-4090},
year = {2010},
refereed = {yes},
length = {8}
}

Henrici's Friendly Monster Identity Revisited

Peter Paule

In: "Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008, Kotsireas, Ilias S.; Zima, Eugene V. (ed.), pp. 155-163. 2010. Springer, 978-3-642-03561-6.
[bib]
@inproceedings{RISC4864,
author = {Peter Paule},
title = {{Henrici's Friendly Monster Identity Revisited}},
booktitle = {{"Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008}},
language = {english},
pages = {155--163},
publisher = {Springer},
isbn_issn = {978-3-642-03561-6},
year = {2010},
editor = {Kotsireas and Ilias S.; Zima and Eugene V.},
refereed = {yes},
length = {9}
}

Chapter Computer Algebra

F. Chyzak and P. Paule

In: NIST's Digital Library of Mathematical Foundations, F. Olver et al. (ed.), pp. 0-0. 2010. 0.
[bib]
@incollection{RISC5622,
author = {F. Chyzak and P. Paule},
title = {{Chapter Computer Algebra}},
booktitle = {{NIST's Digital Library of Mathematical Foundations}},
language = {english},
pages = {0--0},
publisher = {?},
isbn_issn = {0},
year = {2010},
editor = {F. Olver et al.},
refereed = {no},
length = {40}
}

2009

Algorithms in Symbolic Computation

Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler

In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [pdf]
[bib]
@incollection{RISC3845,
author = {Peter Paule and Bruno Buchberger and Lena Kartashova and Manuel Kauers and Carsten Schneider and Franz Winkler},
title = {{Algorithms in Symbolic Computation}},
booktitle = {{Hagenberg Research}},
language = {english},
chapter = {1},
pages = {5--62},
publisher = {Springer},
isbn_issn = {978-3-642-02126-8},
year = {2009},
annote = {2009-00-00-C},
editor = {Bruno Buchberger et al.},
refereed = {no},
length = {58}
}

The Renaissance of Algorithmic Mathematics

Peter Paule

In: Hagenberg Research, Peter Paule (ed.), pp. 6-15. 2009. Springer Berlin-Heidelberg, 978-3-642-02126-8.
[bib]
@incollection{RISC4178,
author = {Peter Paule},
title = {{The Renaissance of Algorithmic Mathematics}},
booktitle = {{Hagenberg Research}},
language = {english},
pages = {6--15},
publisher = {Springer Berlin-Heidelberg},
isbn_issn = {978-3-642-02126-8},
year = {2009},
editor = {Peter Paule},
refereed = {no},
length = {10}
}

2008

Converging to Gosper's Algorithm

William Y. C. Chen, Peter Paule, Husam L. Saad

Adv. in Appl. Math. 41(3), pp. 351-364. 2008. 0196-8858.
[bib]
@article{RISC4865,
author = {William Y. C. Chen and Peter Paule and Husam L. Saad},
title = {{Converging to Gosper's Algorithm}},
language = {english},
journal = {Adv. in Appl. Math.},
volume = {41},
number = {3},
pages = {351--364},
isbn_issn = {0196-8858},
year = {2008},
refereed = {yes},
length = {14}
}

2007

A Computer Proof of Moll's Log-Concavity Conjecture

Manuel Kauers, Peter Paule

Proceedings of the AMS 135(12), pp. 3847-3856. December 2007. ISSN 0002-9939. [ps]
[bib]
@article{RISC2926,
author = {Manuel Kauers and Peter Paule},
title = {{A Computer Proof of Moll's Log-Concavity Conjecture}},
language = {english},
journal = {Proceedings of the AMS},
volume = {135},
number = {12},
pages = {3847--3856},
isbn_issn = {ISSN 0002-9939},
year = {2007},
month = {December},
refereed = {yes},
length = {9}
}

MacMahon's Partition Analysis XI: The Search for Modular Forms

G.E. Andrews and P. Paule

Acta Arithmetica 126, pp. 281-. 2007. 0.
[bib]
@article{RISC5648,
author = {G.E. Andrews and P. Paule},
title = {{MacMahon's Partition Analysis XI: The Search for Modular Forms}},
language = {english},
journal = {Acta Arithmetica 126},
pages = {281--},
isbn_issn = {0},
year = {2007},
refereed = {yes},
length = {14}
}

When is 0.999... equal to 1?

C. Schneider, R. Pemantle

Amer. Math. Monthly 114(4), pp. 344-350. 2007. ISSN 0002-9890. Preliminary version online. [ps] [pdf]
[bib]
@article{RISC2800,
author = {C. Schneider and R. Pemantle},
title = {{When is 0.999... equal to 1?}},
language = {english},
journal = {Amer. Math. Monthly},
volume = {114},
number = {4},
pages = {344--350},
isbn_issn = {ISSN 0002-9890},
year = {2007},
note = {Preliminary version online},
refereed = {yes},
length = {7}
}

Simplifying Sums in ${\Pi}{\Sigma}^*$-Extensions

C. Schneider

J. Algebra Appl. 6(3), pp. 415-441. 2007. ISSN: 0219-4988. Preliminary version online. [ps] [pdf]
[bib]
@article{RISC2953,
author = {C. Schneider},
title = {{Simplifying Sums in ${\Pi}{\Sigma}^*$-Extensions}},
language = {english},
journal = {J. Algebra Appl.},
volume = {6},
number = {3},
pages = {415--441},
isbn_issn = {ISSN: 0219-4988},
year = {2007},
note = {Preliminary version online},
refereed = {yes},
length = {26}
}

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