Computer Algebra for Nested Sums and Products [F050-09]
Project Lead
Project Duration
01/03/2013 - 28/02/2021Project URL
Project WebsitePublications
2018
The Method of Brackets in Experimental Mathematics
Ivan Gonzalez, Karen Kohl, Lin Jiu, and Victor H. Moll
In: Frontiers in Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. -. 2018. World Scientific Publishing, 978-981-3228-87-0. [url]@incollection{RISC5497,
author = {Ivan Gonzalez and Karen Kohl and Lin Jiu and and Victor H. Moll},
title = {{The Method of Brackets in Experimental Mathematics}},
booktitle = {{Frontiers in Orthogonal Polynomials and q-Series}},
language = {english},
pages = {--},
publisher = {World Scientific Publishing},
isbn_issn = {978-981-3228-87-0},
year = {2018},
editor = {Xin Li and Zuhair Nashed},
refereed = {no},
length = {0},
url = {http://www.worldscientific.com/worldscibooks/10.1142/10677}
}
author = {Ivan Gonzalez and Karen Kohl and Lin Jiu and and Victor H. Moll},
title = {{The Method of Brackets in Experimental Mathematics}},
booktitle = {{Frontiers in Orthogonal Polynomials and q-Series}},
language = {english},
pages = {--},
publisher = {World Scientific Publishing},
isbn_issn = {978-981-3228-87-0},
year = {2018},
editor = {Xin Li and Zuhair Nashed},
refereed = {no},
length = {0},
url = {http://www.worldscientific.com/worldscibooks/10.1142/10677}
}
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]@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}
}
Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions
J. Middeke, C. Schneider
In: Advances in Computer Algebra. WWCA 2016., C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 149-173. 2018. Springer, ISSN 2194-1009. arXiv:1705.00280 [cs.SC]. [url]@incollection{RISC5447,
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {149--173},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.00280 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {24},
url = {https://arxiv.org/abs/1705.00280}
}
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {149--173},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.00280 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {24},
url = {https://arxiv.org/abs/1705.00280}
}
Representing (q-)hypergeometric products and mixed versions in difference rings
E.D. Ocansey, C. Schneider
In: Advances in Computer Algebra. WWCA 2016., C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 175-213. 2018. Springer, ISSN 2194-1009. arXiv:1705.01368 [cs.SC]. [url]@incollection{RISC5448,
author = {E.D. Ocansey and C. Schneider},
title = {{Representing (q-)hypergeometric products and mixed versions in difference rings}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {175--213},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.01368 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {36},
url = {https://arxiv.org/abs/1705.01368}
}
author = {E.D. Ocansey and C. Schneider},
title = {{Representing (q-)hypergeometric products and mixed versions in difference rings}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {175--213},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.01368 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {36},
url = {https://arxiv.org/abs/1705.01368}
}
Refined Holonomic Summation Algorithms in Particle Physics
J. Blümlein, M. Round, C. Schneider
In: Advances in Computer Algebra. WWCA 2016., E. Zima, C. Schneider (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 51-91. 2018. Springer, ISSN 2194-1009. arXiv:1706.03677 [cs.SC]. [url]@incollection{RISC5462,
author = {J. Blümlein and M. Round and C. Schneider},
title = {{Refined Holonomic Summation Algorithms in Particle Physics}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics },
volume = {226},
pages = {51--91},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1706.03677 [cs.SC]},
editor = {E. Zima and C. Schneider},
refereed = {yes},
length = {39},
url = {https://arxiv.org/abs/1706.03677}
}
author = {J. Blümlein and M. Round and C. Schneider},
title = {{Refined Holonomic Summation Algorithms in Particle Physics}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics },
volume = {226},
pages = {51--91},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1706.03677 [cs.SC]},
editor = {E. Zima and C. Schneider},
refereed = {yes},
length = {39},
url = {https://arxiv.org/abs/1706.03677}
}
The two-mass contribution to the three-loop pure singlet operator matrix element
J. Ablinger, J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald
Nucl. Phys. B(927), pp. 339-367. 2018. ISSN 0550-3213. arXiv:1711.06717 [hep-ph]. [url]@article{RISC5504,
author = {J. Ablinger and J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The two-mass contribution to the three-loop pure singlet operator matrix element}},
language = {english},
journal = {Nucl. Phys. B},
number = {927},
pages = {339--367},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1711.06717 [hep-ph]},
refereed = {yes},
length = {29},
url = {https://arxiv.org/abs/1711.06717}
}
author = {J. Ablinger and J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The two-mass contribution to the three-loop pure singlet operator matrix element}},
language = {english},
journal = {Nucl. Phys. B},
number = {927},
pages = {339--367},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1711.06717 [hep-ph]},
refereed = {yes},
length = {29},
url = {https://arxiv.org/abs/1711.06717}
}
Algebraic independence of sequences generated by (cyclotomic) harmonic sums
J. Ablinger, C. Schneider
Annals of Combinatorics 22(2), pp. 213-244. 2018. ISSN: 0218-0006. arXiv:1510.03692 [cs.SC], doi 10.1007/s00026-018-0381-5. [url]@article{RISC5507,
author = {J. Ablinger and C. Schneider},
title = {{Algebraic independence of sequences generated by (cyclotomic) harmonic sums}},
language = {english},
journal = {Annals of Combinatorics},
volume = {22},
number = {2},
pages = {213--244},
isbn_issn = {ISSN: 0218-0006},
year = {2018},
note = {arXiv:1510.03692 [cs.SC], doi 10.1007/s00026-018-0381-5},
refereed = {yes},
length = {32},
url = {https://link.springer.com/journal/26/22/2/page/1}
}
author = {J. Ablinger and C. Schneider},
title = {{Algebraic independence of sequences generated by (cyclotomic) harmonic sums}},
language = {english},
journal = {Annals of Combinatorics},
volume = {22},
number = {2},
pages = {213--244},
isbn_issn = {ISSN: 0218-0006},
year = {2018},
note = {arXiv:1510.03692 [cs.SC], doi 10.1007/s00026-018-0381-5},
refereed = {yes},
length = {32},
url = {https://link.springer.com/journal/26/22/2/page/1}
}
The Heavy Quark Form Factors at Two Loops
J. Ablinger, A. Behring, J. Bluemlein, G. Falcioni, A. De Freitas, P. Marquard, N. Rana, C. Schneider
Physical Review D 97(094022), pp. 1-44. 2018. ISSN 1550-2368. arXiv:1712.09889 [hep-ph]. [url]@article{RISC5522,
author = {J. Ablinger and A. Behring and J. Bluemlein and G. Falcioni and A. De Freitas and P. Marquard and N. Rana and C. Schneider},
title = {{The Heavy Quark Form Factors at Two Loops}},
language = {english},
journal = {Physical Review D},
volume = {97},
number = {094022},
pages = {1--44},
isbn_issn = {ISSN 1550-2368},
year = {2018},
note = {arXiv:1712.09889 [hep-ph]},
refereed = {yes},
length = {131},
url = {https://doi.org/10.1103/PhysRevD.97.094022}
}
author = {J. Ablinger and A. Behring and J. Bluemlein and G. Falcioni and A. De Freitas and P. Marquard and N. Rana and C. Schneider},
title = {{The Heavy Quark Form Factors at Two Loops}},
language = {english},
journal = {Physical Review D},
volume = {97},
number = {094022},
pages = {1--44},
isbn_issn = {ISSN 1550-2368},
year = {2018},
note = {arXiv:1712.09889 [hep-ph]},
refereed = {yes},
length = {131},
url = {https://doi.org/10.1103/PhysRevD.97.094022}
}
The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg, Q}^{(3)}$
J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald
Nucl. Phys. B 932, pp. 129-240. 2018. ISSN 0550-3213. arXiv:1804.02226 [hep-ph]. [url]@article{RISC5618,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$}},
language = {english},
journal = {Nucl. Phys. B},
volume = {932},
pages = {129--240},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1804.02226 [hep-ph]},
refereed = {yes},
length = {112},
url = {https://doi.org/10.1016/j.nuclphysb.2018.04.023}
}
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$}},
language = {english},
journal = {Nucl. Phys. B},
volume = {932},
pages = {129--240},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1804.02226 [hep-ph]},
refereed = {yes},
length = {112},
url = {https://doi.org/10.1016/j.nuclphysb.2018.04.023}
}
The Variable Flavor Number Scheme at Next-to-Leading Order
J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald
Physics Letters B 782, pp. 362-366. 2018. ISSN: 0370-2693. arXiv:1804.03129 [hep-ph]. [url]@article{RISC5619,
author = {J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The Variable Flavor Number Scheme at Next-to-Leading Order}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {362--366},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.03129 [hep-ph]},
refereed = {yes},
length = {10},
url = { https://doi.org/10.1016/j.physletb.2018.05.054}
}
author = {J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The Variable Flavor Number Scheme at Next-to-Leading Order}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {362--366},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.03129 [hep-ph]},
refereed = {yes},
length = {10},
url = { https://doi.org/10.1016/j.physletb.2018.05.054}
}
Heavy Quark Form Factors at Three Loops in the Planar Limit
J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider
Physics Letters B 782, pp. 528-532. 2018. ISSN: 0370-2693. arXiv:1804.07313 [hep-ph]. [url]@article{RISC5689,
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Heavy Quark Form Factors at Three Loops in the Planar Limit}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {528--532},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.07313 [hep-ph]},
refereed = {yes},
length = {9},
url = {https://doi.org/10.1016/j.physletb.2018.05.077}
}
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Heavy Quark Form Factors at Three Loops in the Planar Limit}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {528--532},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.07313 [hep-ph]},
refereed = {yes},
length = {9},
url = {https://doi.org/10.1016/j.physletb.2018.05.077}
}
Analytic Computing Methods for Precision Calculations in Quantum Field Theory
J. Blümlein, C. Schneider
INTERNATIONAL JOURNAL OF MODERN PHYSICS A (IJMPA) 33(1830015), pp. 1-35. 2018. ISSN: 1793-656X. [url]@article{RISC5698,
author = {J. Blümlein and C. Schneider},
title = {{Analytic Computing Methods for Precision Calculations in Quantum Field Theory}},
language = {english},
journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A (IJMPA)},
volume = {33},
number = {1830015},
pages = {1--35},
isbn_issn = {ISSN: 1793-656X},
year = {2018},
refereed = {yes},
length = {29},
url = {https://doi.org/10.1142/S0217751X18300156}
}
author = {J. Blümlein and C. Schneider},
title = {{Analytic Computing Methods for Precision Calculations in Quantum Field Theory}},
language = {english},
journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A (IJMPA)},
volume = {33},
number = {1830015},
pages = {1--35},
isbn_issn = {ISSN: 1793-656X},
year = {2018},
refereed = {yes},
length = {29},
url = {https://doi.org/10.1142/S0217751X18300156}
}
The ρ parameter at three loops and elliptic integrals
J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, P. Marquard, C. Schneider
In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, , to appear in PoS , pp. 1-14. 2018. arXiv:1807.05287 [hep-ph].@inproceedings{RISC5722,
author = {J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and P. Marquard and C. Schneider},
title = {{The ρ parameter at three loops and elliptic integrals}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018}},
language = {english},
series = {to appear in PoS},
pages = {1--14},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.05287 [hep-ph]},
editor = {?},
refereed = {yes},
length = {14}
}
author = {J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and P. Marquard and C. Schneider},
title = {{The ρ parameter at three loops and elliptic integrals}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018}},
language = {english},
series = {to appear in PoS},
pages = {1--14},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.05287 [hep-ph]},
editor = {?},
refereed = {yes},
length = {14}
}
Two-mass three-loop effects in deep-inelastic scattering
J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald
In: submitted, , pp. 1-8. 2018. arXiv:1807.07855 [hep-ph]. [url]@inproceedings{RISC5728,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{Two-mass three-loop effects in deep-inelastic scattering}},
booktitle = {{submitted}},
language = {english},
pages = {1--8},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.07855 [hep-ph]},
editor = {?},
refereed = {yes},
length = {8},
url = {https://arxiv.org/abs/1807.07855}
}
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{Two-mass three-loop effects in deep-inelastic scattering}},
booktitle = {{submitted}},
language = {english},
pages = {1--8},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.07855 [hep-ph]},
editor = {?},
refereed = {yes},
length = {8},
url = {https://arxiv.org/abs/1807.07855}
}
2017
Discovering and Proving Infinite Binomial Sums Identities
J. Ablinger
Experimental Mathematics 26(1), pp. 62-71. 2017. ISSN 1058-6458. 10.1080/10586458.2015.1116028. [url]@article{RISC5159,
author = {J. Ablinger},
title = {{Discovering and Proving Infinite Binomial Sums Identities}},
language = {english},
journal = {Experimental Mathematics},
volume = {26},
number = {1},
pages = {62--71},
isbn_issn = {ISSN 1058-6458},
year = {2017},
note = {10.1080/10586458.2015.1116028},
refereed = {yes},
length = {10},
url = {http://arxiv.org/abs/1507.01703}
}
author = {J. Ablinger},
title = {{Discovering and Proving Infinite Binomial Sums Identities}},
language = {english},
journal = {Experimental Mathematics},
volume = {26},
number = {1},
pages = {62--71},
isbn_issn = {ISSN 1058-6458},
year = {2017},
note = {10.1080/10586458.2015.1116028},
refereed = {yes},
length = {10},
url = {http://arxiv.org/abs/1507.01703}
}
Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm
J. Ablinger
In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang and C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-8. 2017. ISSN 1824-8039. arXiv:1801.01039 [cs.SC]. [url]@inproceedings{RISC5527,
author = {J. Ablinger},
title = {{Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm}},
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--8},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1801.01039 [cs.SC]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {8},
url = {https://pos.sissa.it/290/001/pdf}
}
author = {J. Ablinger},
title = {{Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm}},
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--8},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1801.01039 [cs.SC]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {8},
url = {https://pos.sissa.it/290/001/pdf}
}
Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, C. Schneider, F. Wißbrock
Nucl. Phys. B. 921, pp. 585-688. 2017. ISSN 0550-3213. arXiv:1705.07030 [hep-ph]. [url]@article{RISC5451,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Hasselhuhn and C. Schneider and F. Wißbrock},
title = {{Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {921},
pages = {585--688},
isbn_issn = {ISSN 0550-3213},
year = {2017},
note = {arXiv:1705.07030 [hep-ph]},
refereed = {yes},
length = {99},
url = {https://arxiv.org/abs/1705.07030}
}
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Hasselhuhn and C. Schneider and F. Wißbrock},
title = {{Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {921},
pages = {585--688},
isbn_issn = {ISSN 0550-3213},
year = {2017},
note = {arXiv:1705.07030 [hep-ph]},
refereed = {yes},
length = {99},
url = {https://arxiv.org/abs/1705.07030}
}
Integral representations of equally positive integer-indexed harmonic sums at infinity
L. Jiu
Research in Number Theory 3(10), pp. 1-4. 2017. 2363-9555. [url]@article{RISC5385,
author = {L. Jiu},
title = {{Integral representations of equally positive integer-indexed harmonic sums at infinity}},
language = {English},
abstract = {We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special cases coincide with zeta values at positive integer arguments.},
journal = {Research in Number Theory},
volume = {3},
number = {10},
pages = {1--4},
isbn_issn = {2363-9555},
year = {2017},
refereed = {no},
length = {4},
url = {https://resnumtheor.springeropen.com/articles/10.1007/s40993-017-0074-x}
}
author = {L. Jiu},
title = {{Integral representations of equally positive integer-indexed harmonic sums at infinity}},
language = {English},
abstract = {We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special cases coincide with zeta values at positive integer arguments.},
journal = {Research in Number Theory},
volume = {3},
number = {10},
pages = {1--4},
isbn_issn = {2363-9555},
year = {2017},
refereed = {no},
length = {4},
url = {https://resnumtheor.springeropen.com/articles/10.1007/s40993-017-0074-x}
}
An extension of the method of brackets. Part 1
Ivan Gonzalez, Karen Kohl, Lin Jiu, and Victor H. Moll
Open Mathematics (formerly Central European Journal of Mathematics) 15, pp. 1181-1211. 2017. 2391-5455. [url]@article{RISC5483,
author = {Ivan Gonzalez and Karen Kohl and Lin Jiu and and Victor H. Moll},
title = {{An extension of the method of brackets. Part 1}},
language = {english},
abstract = {The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients $a_n$ have meromorphic representations for $n\in\mathbb{C}$, but might vanish or blow up when $n\in\mathbb{N}$. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.},
journal = {Open Mathematics (formerly Central European Journal of Mathematics)},
volume = {15},
pages = {1181--1211},
isbn_issn = {2391-5455},
year = {2017},
refereed = {no},
length = {31},
url = {https://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0100/math-2017-0100.xml?format=INT}
}
author = {Ivan Gonzalez and Karen Kohl and Lin Jiu and and Victor H. Moll},
title = {{An extension of the method of brackets. Part 1}},
language = {english},
abstract = {The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients $a_n$ have meromorphic representations for $n\in\mathbb{C}$, but might vanish or blow up when $n\in\mathbb{N}$. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.},
journal = {Open Mathematics (formerly Central European Journal of Mathematics)},
volume = {15},
pages = {1181--1211},
isbn_issn = {2391-5455},
year = {2017},
refereed = {no},
length = {31},
url = {https://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0100/math-2017-0100.xml?format=INT}
}
Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K
Johannes Middeke
In: Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, Michael Burr (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 325-332. 2017. 978-1-4503-5064-8.@inproceedings{RISC5489,
author = {Johannes Middeke},
title = {{Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K}},
booktitle = {{Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
abstract = {We consider systems A_ell(t )y(q^ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.},
pages = {325--332},
isbn_issn = {978-1-4503-5064-8},
year = {2017},
editor = {Michael Burr},
refereed = {yes},
length = {7},
conferencename = {International Symposium on Symbolic and Algebraic Computation}
}
author = {Johannes Middeke},
title = {{Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K}},
booktitle = {{Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
abstract = {We consider systems A_ell(t )y(q^ell t ) + . . . + A 0 (t )y(t ) = b (t ) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t ) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.},
pages = {325--332},
isbn_issn = {978-1-4503-5064-8},
year = {2017},
editor = {Michael Burr},
refereed = {yes},
length = {7},
conferencename = {International Symposium on Symbolic and Algebraic Computation}
}
