Mag. Burkhard Zimmermann

Research Area

Definite Symbolic Summation and Integration of Holonomic Functions

Office

Schloss Hagenberg
A-4232 Hagenberg im Mühlkreis

Room:

Postal Address

Research Institute for Symbolic Computation
Johannes Kepler University
Altenberger Straße 69
A-4040 Linz, Austria

eMail

Burkhard.Zimmermann@risc.jku.at

Software

Dependencies

A Mathematica Package for Computing Algebraic Relations of C-finite Sequences and Multi-Sequences

This package is part of the RISCErgoSum bundle. For any tuple f_1, f_2,..., f_r of sequences, the set of multivariate polynomials p such that p(f1(n),f2(n),...,fr(n))=0 for all points n forms ...

Authors: Manuel Kauers, Burkhard Zimmermann

More Software Website

This package is part of the RISCErgoSum bundle. Engel is a Mathematica implementation of the q -Engel Expansion algorithm which expands q-series into inverse polynomial series. Examples of q-Engel Expansions include the Rogers-Ramanujan identities together with their elegant generalization by ...

Authors: Burkhard Zimmermann

More Software Website

Publications

2013

[Zimmermann]

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]. [doi] [pdf]

[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 = {https://www.doi.org/10.1007/978-3-7091-1616-6_3}
}

2008

[Zimmermann]

Computing the complexity for schelling segregation models

S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann

Communications in Nonlinear Science and Numerical Simulations 13, pp. 2236-2245. 2008. ISSN 1007-5704. [doi] [pdf]

[bib]

@article{RISC3104,
author = {S. Gerhold and L. Glebsky and C. Schneider and H. Weiss and B. Zimmermann},
title = {{Computing the complexity for schelling segregation models}},
language = {english},
journal = {Communications in Nonlinear Science and Numerical Simulations},
volume = {13},
pages = {2236--2245},
isbn_issn = {ISSN 1007-5704},
year = {2008},
refereed = {yes},
length = {10},
url = {https://doi.org/10.1016/j.cnsns.2007.04.023}
}

[Zimmermann]

Computing the Algebraic Relations of C-finite Sequences and Multisequences

Manuel Kauers, Burkhard Zimmermann

Journal of Symbolic Computation 43(11), pp. 787-803. 2008. ISSN 0747-7171.. [ps] [pdf]

[bib]

@article{RISC3341,
author = {Manuel Kauers and Burkhard Zimmermann},
title = {{Computing the Algebraic Relations of C-finite Sequences and Multisequences}},
language = {english},
abstract = {We present an algorithm for computing generators for the ideal of algebraic relations among sequences which are given by homogeneous linear recurrence equations with constant coefficients. Knowing these generators makes it possible to use Groebner bases methods for carrying out certain basic operations in the ring of such sequences effectively. In particular, one can answer the question whether a given sequence can be represented in terms of other given sequences. },
journal = {Journal of Symbolic Computation},
volume = {43},
number = {11},
pages = {787--803},
isbn_issn = {ISSN 0747-7171.},
year = {2008},
refereed = {yes},
length = {25}
}

2006

[Zimmermann]

Limit States for One-dimensional Schelling Segregation Models

S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann

J. Kepler University, Linz. Technical report no. 2006-39, 2006. SFB-Report. [pdf]

[bib]

@techreport{RISC3004,
author = {S.~Gerhold and L.~Glebsky and C.~Schneider and H.~Weiss and B.~Zimmermann},
title = {{Limit States for One-dimensional Schelling Segregation Models}},
language = {english},
number = {2006-39},
year = {2006},
institution = {J.~Kepler University, Linz},
length = {13},
type = {SFB-Report}
}

[Zimmermann]

On the number of distinct multinomial coefficients

George E. Andrews, Arnold Knopfmacher, Burkhard Zimmermann

Journal of Number Theory 118(1), pp. 15-30. May 2006. ISSN 0022-314X. [pdf]

[bib]

@article{RISC3073,
author = {George~E.~Andrews and Arnold~Knopfmacher and Burkhard~Zimmermann},
title = {{On the number of distinct multinomial coefficients}},
language = {english},
journal = {Journal of Number Theory},
volume = {118},
number = {1},
pages = {15--30},
isbn_issn = {ISSN 0022-314X},
year = {2006},
month = {May},
refereed = {yes},
length = {16}
}

2004

[Zimmermann]

Computer Proofs of Matrix Product Identities

P.J. Larcombe, A. Riese, B. Zimmermann

J. Algebra Appl. 3, pp. 105-109. 2004. ISSN 0219-4988. [pdf]

[bib]

@article{RISC428,
author = {P.J. Larcombe and A. Riese and B. Zimmermann},
title = {{Computer Proofs of Matrix Product Identities}},
language = {english},
journal = {J. Algebra Appl.},
volume = {3},
pages = {105--109},
isbn_issn = {ISSN 0219-4988},
year = {2004},
refereed = {yes},
length = {5}
}

2001

[Zimmermann]

The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval

F. Chyzak, P. Paule, O. Scherzer, A. Schoisswohl, B. Zimmermann

Experiment. Math. 10, pp. 67-86. 2001. ISSN 1058-6458. [pdf]

[bib]

@article{RISC2060,
author = {F. Chyzak and P. Paule and O. Scherzer and A. Schoisswohl and B. Zimmermann},
title = {{The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval}},
language = {english},
journal = {Experiment. Math.},
volume = {10},
pages = {67--86},
isbn_issn = {ISSN 1058-6458},
year = {2001},
refereed = {yes},
length = {20}
}

[Zimmermann]

Engel Expansions of $q$-Series by Computer Algebra

G.E. Andrews, A. Knopfmacher, P. Paule, B. Zimmermann

In: Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F.G. Garvan and M.E.H. Ismail (ed.), Developments in Mathematics 4, pp. 33-57. 2001. Kluwer, ISBN: 1402001010. [pdf]

[bib]

@inproceedings{RISC2065,
author = {G.E. Andrews and A. Knopfmacher and P. Paule and B. Zimmermann},
title = {{Engel Expansions of $q$-Series by Computer Algebra}},
booktitle = {{Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics}},
language = {english},
series = {Developments in Mathematics},
volume = {4},
pages = {33--57},
publisher = {Kluwer},
isbn_issn = {ISBN: 1402001010},
year = {2001},
editor = {F.G. Garvan and M.E.H. Ismail},
refereed = {yes},
length = {25}
}

2000

[Zimmermann]

Difference Forms and Hypergeometric Sums

Burkhard Zimmermann

Technical report no. 00-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). February 2000. Master Thesis. [ps]

[bib]

@techreport{RISC1544,
author = {Burkhard Zimmermann},
title = {{Difference Forms and Hypergeometric Sums}},
language = {english},
number = {00-02},
year = {2000},
month = {February},
note = {Master Thesis},
keywords = {multisum identities},
sponsor = {FWF},
length = {0},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}