### Computer Algebra Tools for Special Functions [DK6]

Project Lead: Peter Paule

Skip to content# DI Clemens Gunter Raab

### Research Area

Symbolic Integration## Ongoing Projects

### Computer Algebra Tools for Special Functions [DK6]

Project Duration: 01/10/2011 - 31/12/2020MoreProject Website## Publications

All 2019 - 2017 2016 - 2014 2013 - 2011 2010 - 2008 2007 - 2005 2004 - 2002 2001 - 1999 1998 - 1996 1995 - 1993 1992 - 1990 1989 - 1987 1986 - 1965 ### 2018

### Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

#### J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C.G. Raab, C.-S. Radu, C. Schneider

J. Math. Phys. 59(062305), pp. 1-55. 2018. ISSN 0022-2488. arXiv:1706.01299 [hep-th]. [url]### 2017

### Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2017. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url]### 2015

### 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, S. Schneider, F. Wißbrock

In: 17th International Conference in Quantum Chromodynamics (QCD 14), Stephan Narison (ed.), Nucl. Phys. B (Proc. Suppl.) 258-259, pp. 41-44. 2015. ISSN 0550-3213. arXiv:1409.1804 [hep-ph]. [url]### 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C.G. Raab, M. Round, C. Schneider, F. Wißbrock

In: Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP), PoS(EPS-HEP2015)504, pp. 1-13. 2015. ISSN 1824-8039. arXiv:1602.00583 [hep-ph]. [url]### 2014

### Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms

#### J. Ablinger, J. Blümlein, C. Raab, C. Schneider, F. Wissbrock

Nuclear Physics B 885, pp. 409-447. 2014. ISSN: 0550-3213. arXiv:1403.1137 [hep-ph]. [url]### Iterated Binomial Sums and their Associated Iterated Integrals

#### J. Ablinger, J. Blümlein, C.G. Raab, C. Schneider

J. Math. Phys. 55(112301), pp. 1-57. 2014. ISSN 0022-2488. arXiv:1407.1822 [hep-th]. [url]### Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wißbrock

In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)041 , pp. 1-11. 2014. ISSN 1824-8039. arXiv:1407.3638 [hep-ph]. [url]### Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

#### J. Ablinger, J. Blümlein, C G. Raab, C. Schneider

In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)020 , pp. 1-13. 2014. ISSN 1824-8039. arXiv:1407.4721 [hep-th]. [url]### Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums

#### J. Blümlein, I. Dubovyk, J. Gluza, M. Ochman, C.G. Raab, T. Riemann, C. Schneider

In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)52 , pp. 1-14. 2014. ISSN 1824-8039. arXiv:1407.7832 [hep-ph]. [url]### 2013

### Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

#### J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wissbrock

In: XXI International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2013, PoS(DIS 2013)301, pp. 1-8. 2013. ISSN 1824-8039. arXiv:1307.7548 [hep-ph]. [url]### New Results on the 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering

#### A. Behring, J. Bluemlein, A. De Freitas, T. Pfoh, C. Raab, M. Round, J. Ablinger, A. Hasselhuhn, C. Schneider, F. Wissbrock, A. von Manteuffel

In: Proc. of RADCOR, , PoS(RADCOR 2013)058 , pp. 1-21. 2013. ISSN 1824-8039. arXiv:1312.0124 [hep-ph]. [url]### 2012

### Using Groebner bases for finding the logarithmic part of the integral of transcendental functions

#### Clemens G. Raab

Journal of Symbolic Computation 47(10), pp. 1290-1296. 2012. ISSN 0747-7171.### Solving Linear Ordinary Differential Systems in Hyperexponential Extensions

#### Moulay A. Barkatou, Clemens G. Raab

In: Proceedings of ISSAC 2012, Joris van der Hoeven and Mark van Hoeij (ed.), Proceedings of 37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012, pp. 51-58. 2012. ISBN 978-1-4503-1269. [pdf]### Definite Integration in Differential Fields

#### Clemens G. Raab

Johannes Kepler Universität Linz, Austria. PhD Thesis. August 2012. [pdf]### Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N

#### J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, S. Klein, C. Raab, M. Round, C. Schneider, F. Wissbrock

In: Proc. Loops and Legs in Quantum Field Theory 2012, J. Blümlein, S. Moch, T. Riemann (ed.), PoS(LL2012)033 , pp. 1-12. 2012. ISSN 1824-8039. [url]### 2008

### Symbolic Computations for Nonlinear Wave Resonances

#### E. Kartashova, C. Raab, Ch. Feurer, G. Mayrhofer, W. Schreiner

In: "Extreme Ocean Waves", E. Pelinovsky, Ch. Kharif (ed.), pp. 97-128. 2008. Springer, ISBN: 978-1-4020-8313-6. [url] [pdf]

Project Lead: Peter Paule

[Raab]

@**article**{RISC5456,

author = {J. Ablinger and J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams}},

language = {english},

journal = {J. Math. Phys.},

volume = {59},

number = {062305},

pages = {1--55},

isbn_issn = {ISSN 0022-2488},

year = {2018},

note = {arXiv:1706.01299 [hep-th]},

refereed = {no},

length = {55},

url = {https://arxiv.org/abs/1706.01299}

}

author = {J. Ablinger and J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams}},

language = {english},

journal = {J. Math. Phys.},

volume = {59},

number = {062305},

pages = {1--55},

isbn_issn = {ISSN 0022-2488},

year = {2018},

note = {arXiv:1706.01299 [hep-th]},

refereed = {no},

length = {55},

url = {https://arxiv.org/abs/1706.01299}

}

[Raab]

@**inproceedings**{RISC5350,

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://pos.sissa.it/290/069/pdf}

}

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://pos.sissa.it/290/069/pdf}

}

[Raab]

@**inproceedings**{RISC5060,

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and S. Schneider and F. Wißbrock},

title = {{3-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{17th International Conference in Quantum Chromodynamics (QCD 14)}},

language = {english},

series = {Nucl. Phys. B (Proc. Suppl.)},

volume = {258-259},

pages = {41--44},

isbn_issn = {ISSN 0550-3213},

year = {2015},

note = { arXiv:1409.1804 [hep-ph]},

editor = {Stephan Narison},

refereed = {yes},

length = {4},

url = {http://arxiv.org/abs/arXiv:1409.1804}

}

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and S. Schneider and F. Wißbrock},

title = {{3-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{17th International Conference in Quantum Chromodynamics (QCD 14)}},

language = {english},

series = {Nucl. Phys. B (Proc. Suppl.)},

volume = {258-259},

pages = {41--44},

isbn_issn = {ISSN 0550-3213},

year = {2015},

note = { arXiv:1409.1804 [hep-ph]},

editor = {Stephan Narison},

refereed = {yes},

length = {4},

url = {http://arxiv.org/abs/arXiv:1409.1804}

}

[Raab]

@**inproceedings**{RISC5247,

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C.G. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP)}},

language = {english},

volume = {PoS(EPS-HEP2015)504},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2015},

note = {arXiv:1602.00583 [hep-ph]},

editor = {?},

refereed = {yes},

length = {13},

url = {http://pos.sissa.it/archive/conferences/234/504/EPS-HEP2015_504.pdf}

}

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C.G. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP)}},

language = {english},

volume = {PoS(EPS-HEP2015)504},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2015},

note = {arXiv:1602.00583 [hep-ph]},

editor = {?},

refereed = {yes},

length = {13},

url = {http://pos.sissa.it/archive/conferences/234/504/EPS-HEP2015_504.pdf}

}

[Raab]

@**article**{RISC4960,

author = {J. Ablinger and J. Blümlein and C. Raab and C. Schneider and F. Wissbrock},

title = {{Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms}},

language = {english},

journal = {Nuclear Physics B},

volume = {885},

pages = {409--447},

isbn_issn = {ISSN: 0550-3213},

year = {2014},

note = { arXiv:1403.1137 [hep-ph]},

refereed = {yes},

length = {39},

url = {http://arxiv.org/abs/1403.1137}

}

author = {J. Ablinger and J. Blümlein and C. Raab and C. Schneider and F. Wissbrock},

title = {{Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms}},

language = {english},

journal = {Nuclear Physics B},

volume = {885},

pages = {409--447},

isbn_issn = {ISSN: 0550-3213},

year = {2014},

note = { arXiv:1403.1137 [hep-ph]},

refereed = {yes},

length = {39},

url = {http://arxiv.org/abs/1403.1137}

}

[Raab]

@**article**{RISC5013,

author = {J. Ablinger and J. Blümlein and C.G. Raab and C. Schneider},

title = {{Iterated Binomial Sums and their Associated Iterated Integrals}},

language = {english},

journal = {J. Math. Phys.},

volume = {55},

number = {112301},

pages = {1--57},

isbn_issn = {ISSN 0022-2488},

year = {2014},

note = {arXiv:1407.1822 [hep-th]},

refereed = {yes},

length = {57},

url = {http://dx.doi.org/10.1063/1.4900836}

}

author = {J. Ablinger and J. Blümlein and C.G. Raab and C. Schneider},

title = {{Iterated Binomial Sums and their Associated Iterated Integrals}},

language = {english},

journal = {J. Math. Phys.},

volume = {55},

number = {112301},

pages = {1--57},

isbn_issn = {ISSN 0022-2488},

year = {2014},

note = {arXiv:1407.1822 [hep-th]},

refereed = {yes},

length = {57},

url = {http://dx.doi.org/10.1063/1.4900836}

}

[Raab]

@**inproceedings**{RISC5023,

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)041},

pages = {1--11},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.3638 [hep-ph]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {11},

url = {http://arxiv.org/abs/1407.3638}

}

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)041},

pages = {1--11},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.3638 [hep-ph]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {11},

url = {http://arxiv.org/abs/1407.3638}

}

[Raab]

@**inproceedings**{RISC5024,

author = {J. Ablinger and J. Blümlein and C G. Raab and C. Schneider},

title = {{Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)020},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.4721 [hep-th]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {13},

url = {http://arxiv.org/abs/1407.4721}

}

author = {J. Ablinger and J. Blümlein and C G. Raab and C. Schneider},

title = {{Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)020},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.4721 [hep-th]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {13},

url = {http://arxiv.org/abs/1407.4721}

}

[Raab]

@**inproceedings**{RISC5032,

author = {J. Blümlein and I. Dubovyk and J. Gluza and M. Ochman and C.G. Raab and T. Riemann and C. Schneider},

title = {{Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)52},

pages = {1--14},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.7832 [hep-ph]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {14},

url = {http://arxiv.org/abs/1407.7832}

}

author = {J. Blümlein and I. Dubovyk and J. Gluza and M. Ochman and C.G. Raab and T. Riemann and C. Schneider},

title = {{Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums}},

booktitle = {{Loops and Legs in Quantum Field Theory - LL 2014}},

language = {english},

series = {PoS(LL2014)52},

pages = {1--14},

isbn_issn = {ISSN 1824-8039},

year = {2014},

note = {arXiv:1407.7832 [hep-ph]},

editor = {J. Bluemlein and P. Marquard and T. Riemann},

refereed = {yes},

length = {14},

url = {http://arxiv.org/abs/1407.7832}

}

[Raab]

@**inproceedings**{RISC4760,

author = {J. Ablinger and J. Bluemlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and C. Schneider and F. Wissbrock},

title = {{Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{XXI International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2013}},

language = {english},

volume = {PoS(DIS 2013)301},

pages = {1--8},

isbn_issn = {ISSN 1824-8039},

year = {2013},

note = {arXiv:1307.7548 [hep-ph]},

editor = {?},

refereed = {no},

length = {8},

url = {http://pos.sissa.it/archive/conferences/191/301/DIS%202013_301.pdf}

}

author = {J. Ablinger and J. Bluemlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and C. Schneider and F. Wissbrock},

title = {{Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{XXI International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2013}},

language = {english},

volume = {PoS(DIS 2013)301},

pages = {1--8},

isbn_issn = {ISSN 1824-8039},

year = {2013},

note = {arXiv:1307.7548 [hep-ph]},

editor = {?},

refereed = {no},

length = {8},

url = {http://pos.sissa.it/archive/conferences/191/301/DIS%202013_301.pdf}

}

[Raab]

@**inproceedings**{RISC4875,

author = {A. Behring and J. Bluemlein and A. De Freitas and T. Pfoh and C. Raab and M. Round and J. Ablinger and A. Hasselhuhn and C. Schneider and F. Wissbrock and A. von Manteuffel},

title = {{New Results on the 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering}},

booktitle = {{Proc. of RADCOR}},

language = {english},

series = {PoS(RADCOR 2013)058},

pages = {1--21},

isbn_issn = {ISSN 1824-8039},

year = {2013},

note = {arXiv:1312.0124 [hep-ph]},

editor = {?},

refereed = {yes},

length = {21},

url = {http://arxiv.org/abs/1312.0124}

}

author = {A. Behring and J. Bluemlein and A. De Freitas and T. Pfoh and C. Raab and M. Round and J. Ablinger and A. Hasselhuhn and C. Schneider and F. Wissbrock and A. von Manteuffel},

title = {{New Results on the 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering}},

booktitle = {{Proc. of RADCOR}},

language = {english},

series = {PoS(RADCOR 2013)058},

pages = {1--21},

isbn_issn = {ISSN 1824-8039},

year = {2013},

note = {arXiv:1312.0124 [hep-ph]},

editor = {?},

refereed = {yes},

length = {21},

url = {http://arxiv.org/abs/1312.0124}

}

[Raab]

@**article**{RISC4347,

author = {Clemens G. Raab},

title = {{Using Groebner bases for finding the logarithmic part of the integral of transcendental functions}},

language = {english},

abstract = {We show that Czichowski's algorithm for computing the logarithmic part of the integral of a rational function can be carried over to a rather general class of transcendental functions. Also an asymptotic bound on the number of field operations needed is given.},

journal = {Journal of Symbolic Computation},

volume = {47},

number = {10},

pages = {1290--1296},

isbn_issn = {ISSN 0747-7171},

year = {2012},

refereed = {yes},

keywords = {Symbolic Integration, Elementary Integral, Differential Algebra, Groebner Basis, Special Functions},

length = {7}

}

author = {Clemens G. Raab},

title = {{Using Groebner bases for finding the logarithmic part of the integral of transcendental functions}},

language = {english},

abstract = {We show that Czichowski's algorithm for computing the logarithmic part of the integral of a rational function can be carried over to a rather general class of transcendental functions. Also an asymptotic bound on the number of field operations needed is given.},

journal = {Journal of Symbolic Computation},

volume = {47},

number = {10},

pages = {1290--1296},

isbn_issn = {ISSN 0747-7171},

year = {2012},

refereed = {yes},

keywords = {Symbolic Integration, Elementary Integral, Differential Algebra, Groebner Basis, Special Functions},

length = {7}

}

[Raab]

@**inproceedings**{RISC4582,

author = {Moulay A. Barkatou and Clemens G. Raab},

title = {{Solving Linear Ordinary Differential Systems in Hyperexponential Extensions}},

booktitle = {{Proceedings of ISSAC 2012}},

language = {english},

abstract = {Let F be a differential field generated from the rational functions over some constant field by one hyperexponential extension. We present an algorithm to compute the solutions in F^n of systems of n first-order linear ODEs. Solutions in F of a scalar ODE of higher order can be determined by an algorithm of Bronstein and Fredet. Our approach avoids reduction to the scalar case. We also give examples to show how this can be applied to integration.},

pages = {51--58},

isbn_issn = {ISBN 978-1-4503-1269},

year = {2012},

editor = {Joris van der Hoeven and Mark van Hoeij},

refereed = {yes},

keywords = {Linear Differential Equations over hyperexponential extension, Closed form solutions, Computer Algebra},

sponsor = {Austrian Science Fund (FWF)},

length = {8},

conferencename = {37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012}

}

author = {Moulay A. Barkatou and Clemens G. Raab},

title = {{Solving Linear Ordinary Differential Systems in Hyperexponential Extensions}},

booktitle = {{Proceedings of ISSAC 2012}},

language = {english},

abstract = {Let F be a differential field generated from the rational functions over some constant field by one hyperexponential extension. We present an algorithm to compute the solutions in F^n of systems of n first-order linear ODEs. Solutions in F of a scalar ODE of higher order can be determined by an algorithm of Bronstein and Fredet. Our approach avoids reduction to the scalar case. We also give examples to show how this can be applied to integration.},

pages = {51--58},

isbn_issn = {ISBN 978-1-4503-1269},

year = {2012},

editor = {Joris van der Hoeven and Mark van Hoeij},

refereed = {yes},

keywords = {Linear Differential Equations over hyperexponential extension, Closed form solutions, Computer Algebra},

sponsor = {Austrian Science Fund (FWF)},

length = {8},

conferencename = {37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012}

}

[Raab]

@**phdthesis**{RISC4583,

author = {Clemens G. Raab},

title = {{Definite Integration in Differential Fields}},

language = {english},

abstract = {The general goal of this thesis is to investigate and develop computer algebra tools for the simplification resp. evaluation of definite integrals. One way of finding the value of a definite integral is via the evaluation of an antiderivative of the integrand. If no antiderivative of suitable form is available and the integral depends on additional parameters, then linear relations that are satisfied by the parameter integral of interest may be found based on the principle of parametric integration (often called differentiating under the integral sign or creative telescoping). The main result of this thesis extends results of Risch, Singer, and Bronstein to a complete algorithm for parametric elementary integration for a certain class of integrands covering a majority of the special functions appearing in practice such as orthogonal polynomials, polylogarithms, Bessel functions, etc. A general framework is provided to model those functions in terms of suitable differential fields. Additionally, a generalization of Czichowski's algorithm for computing the logarithmic part of the integral is presented. Moreover, also partial generalizations to include other types of integrands are treated. As subproblems of the integration algorithm one also has to find solutions of linear ordinary differential equations of a certain type. Some contributions are also made to solve those problems in our setting, where the results directly dealing with systems of differential equations have been joint work with Moulay A. Barkatou. For the case of Liouvillian integrands we implemented the algorithm in form of our Mathematica package Integrator. Parts of the implementation also deal with more general functions. Our procedures can be applied to a significant amount of the entries in integral tables, both indefinite and definite integrals. In addition, our procedures have been successfully applied to interesting examples of integrals that do not appear in these tables or for which current standard computer algebra systems like Mathematica or Maple do not succeed. We also give examples of how parameter integrals coming from the work of other researchers can be solved with the software, e.g., an integral arising in analyzing the entropy of certain processes.},

year = {2012},

month = {August},

translation = {0},

school = {Johannes Kepler Universität Linz, Austria},

length = {127}

}

author = {Clemens G. Raab},

title = {{Definite Integration in Differential Fields}},

language = {english},

abstract = {The general goal of this thesis is to investigate and develop computer algebra tools for the simplification resp. evaluation of definite integrals. One way of finding the value of a definite integral is via the evaluation of an antiderivative of the integrand. If no antiderivative of suitable form is available and the integral depends on additional parameters, then linear relations that are satisfied by the parameter integral of interest may be found based on the principle of parametric integration (often called differentiating under the integral sign or creative telescoping). The main result of this thesis extends results of Risch, Singer, and Bronstein to a complete algorithm for parametric elementary integration for a certain class of integrands covering a majority of the special functions appearing in practice such as orthogonal polynomials, polylogarithms, Bessel functions, etc. A general framework is provided to model those functions in terms of suitable differential fields. Additionally, a generalization of Czichowski's algorithm for computing the logarithmic part of the integral is presented. Moreover, also partial generalizations to include other types of integrands are treated. As subproblems of the integration algorithm one also has to find solutions of linear ordinary differential equations of a certain type. Some contributions are also made to solve those problems in our setting, where the results directly dealing with systems of differential equations have been joint work with Moulay A. Barkatou. For the case of Liouvillian integrands we implemented the algorithm in form of our Mathematica package Integrator. Parts of the implementation also deal with more general functions. Our procedures can be applied to a significant amount of the entries in integral tables, both indefinite and definite integrals. In addition, our procedures have been successfully applied to interesting examples of integrals that do not appear in these tables or for which current standard computer algebra systems like Mathematica or Maple do not succeed. We also give examples of how parameter integrals coming from the work of other researchers can be solved with the software, e.g., an integral arising in analyzing the entropy of certain processes.},

year = {2012},

month = {August},

translation = {0},

school = {Johannes Kepler Universität Linz, Austria},

length = {127}

}

[Raab]

@**inproceedings**{RISC4614,

author = {J. Ablinger and J. Bluemlein and A. De Freitas and A. Hasselhuhn and S. Klein and C. Raab and M. Round and C. Schneider and F. Wissbrock},

title = {{Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N}},

booktitle = {{Proc. Loops and Legs in Quantum Field Theory 2012}},

language = {english},

series = {PoS(LL2012)033},

pages = {1--12},

isbn_issn = { ISSN 1824-8039},

year = {2012},

editor = { J. Blümlein and S. Moch and T. Riemann},

refereed = {yes},

length = {12},

url = {http://arxiv.org/abs/1212.6823}

}

author = {J. Ablinger and J. Bluemlein and A. De Freitas and A. Hasselhuhn and S. Klein and C. Raab and M. Round and C. Schneider and F. Wissbrock},

title = {{Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N}},

booktitle = {{Proc. Loops and Legs in Quantum Field Theory 2012}},

language = {english},

series = {PoS(LL2012)033},

pages = {1--12},

isbn_issn = { ISSN 1824-8039},

year = {2012},

editor = { J. Blümlein and S. Moch and T. Riemann},

refereed = {yes},

length = {12},

url = {http://arxiv.org/abs/1212.6823}

}

[Raab]

@**incollection**{RISC3344,

author = {E. Kartashova and C. Raab and Ch. Feurer and G. Mayrhofer and W. Schreiner},

title = {{Symbolic Computations for Nonlinear Wave Resonances}},

booktitle = {{"Extreme Ocean Waves"}},

language = {english},

abstract = {Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations from only locally available software to Web-based services that can be accessed from any computer in the Internet that is equipped with a Web browser. In particular, the results are not bound to the current Mathematica implementation but can be adapted to any other computer algebra system (e.g. Maple) or numerical software system (e.g.MATLAB) of similar expressiveness. Barotropic vorticity equation (=Hasegawa-Mima equation) with zero boundary conditions on a square is taken as a main example.},

pages = {97--128},

publisher = {Springer},

isbn_issn = {ISBN: 978-1-4020-8313-6},

year = {2008},

editor = {E. Pelinovsky and Ch. Kharif},

refereed = {yes},

length = {31},

url = {http://www.springer.com/geosciences/oceanography/book/978-1-4020-8313-6}

}

author = {E. Kartashova and C. Raab and Ch. Feurer and G. Mayrhofer and W. Schreiner},

title = {{Symbolic Computations for Nonlinear Wave Resonances}},

booktitle = {{"Extreme Ocean Waves"}},

language = {english},

abstract = {Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations from only locally available software to Web-based services that can be accessed from any computer in the Internet that is equipped with a Web browser. In particular, the results are not bound to the current Mathematica implementation but can be adapted to any other computer algebra system (e.g. Maple) or numerical software system (e.g.MATLAB) of similar expressiveness. Barotropic vorticity equation (=Hasegawa-Mima equation) with zero boundary conditions on a square is taken as a main example.},

pages = {97--128},

publisher = {Springer},

isbn_issn = {ISBN: 978-1-4020-8313-6},

year = {2008},

editor = {E. Pelinovsky and Ch. Kharif},

refereed = {yes},

length = {31},

url = {http://www.springer.com/geosciences/oceanography/book/978-1-4020-8313-6}

}

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Research Institute for Symbolic Computation (RISC)

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Research Institute for Symbolic Computation (RISC)

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