Holonomic Tools for Basic Hypergeometric Functions
Christoph Koutschan, Peter Paule
In: Frontiers of Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. ?-?. 2018. World Scientific Publishing, ISBN 978-981-3228-87-0. [pdf][bib]
@incollection{RISC5246,
author = {Christoph Koutschan and Peter Paule},
title = {{Holonomic Tools for Basic Hypergeometric Functions}},
booktitle = {{Frontiers of Orthogonal Polynomials and q-Series}},
language = {english},
pages = {?--?},
publisher = {World Scientific Publishing},
isbn_issn = {ISBN 978-981-3228-87-0},
year = {2018},
editor = {Xin Li and Zuhair Nashed},
refereed = {no},
length = {19}
}
Towards a symbolic summation theory for unspecified sequences
P. Paule, C. Schneider
In: To appear in Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, P. Paule, C. Schneider (ed.), Texts and Monographs in Symbolic Computation , pp. 1-37. 2018. Springer, arXiv:1809.06578 [cs.SC]. [url][bib]
@incollection{RISC5750,
author = {P. Paule and C. Schneider},
title = {{Towards a symbolic summation theory for unspecified sequences}},
booktitle = {{To appear in Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
pages = {1--37},
publisher = {Springer},
isbn_issn = {?},
year = {2018},
note = {arXiv:1809.06578 [cs.SC]},
editor = {J. Blümlein and P. Paule and C. Schneider},
refereed = {yes},
length = {37},
url = {https://arxiv.org/abs/1809.06578}
}
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}
}
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: status submitted, , pp. -. 2016. [pdf][bib]
@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A New Witness Identity for $11|p(11n+6)$}},
booktitle = {{status submitted}},
language = {english},
pages = {--},
isbn_issn = { },
year = {2016},
editor = { },
refereed = {yes},
length = {11}
}
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}
}
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}
}
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}
}
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}
}
The Andrews-Sellers Family of Partition Congruences
Peter Paule, Cristian-Silviu Radu
Advances in Mathematics, pp. 819-838. 2012. 0001-8708. [pdf][bib]
@article{RISC4550,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{The Andrews-Sellers Family of Partition Congruences}},
language = {english},
journal = {Advances in Mathematics},
pages = {819--838},
isbn_issn = {0001-8708},
year = {2012},
refereed = {yes},
length = {20}
}
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}
}
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}
}
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}
}
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}
}
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}
}
Computer Algebra
F. Chyzak, P. Paule
In: The Digital Library of Mathematical Functions (DLMF), D. Lozier (ed.), pp. n/a-n/a. 2007. National Institute of Standards and Technology (NIST), Gaithersburg, U.S.A., electronic. In preparation.[bib]
@incollection{RISC2081,
author = {F. Chyzak and P. Paule},
title = {{Computer Algebra}},
booktitle = {{The Digital Library of Mathematical Functions (DLMF)}},
language = {english},
pages = {n/a--n/a},
publisher = {National Institute of Standards and Technology (NIST)},
address = {Gaithersburg, U.S.A.},
isbn_issn = {electronic},
year = {2007},
note = {In preparation},
editor = {D. Lozier},
refereed = {yes},
length = {40}
}
