Computer Algebra for Nested Sums and Products [F050-09]

@article{RISC5896,
author = {J. Ablinger},
title = {{Discovering and Proving Infinite Pochhammer Sum Identities}},
language = {english},
journal = {submitted},
pages = {1--21},
isbn_issn = {?},
year = {2019},
note = {arXiv:1902.11001 [math.CO]},
refereed = {yes},
length = {21},
url = {http://arxiv.org/abs/1902.11001}
}

@article{RISC5801,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities }},
language = {english},
abstract = {We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem. },
journal = {ArXiv e-prints (accepted)},
pages = {1--10},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {10},
url = {https://arxiv.org/abs/1810.12048}
}

@article{RISC5898,
author = {Ali Kemal Uncu},
title = {{A Polynomial Identity Implying Schur's Partition Theorem }},
language = {english},
abstract = {We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz. We also present some related polynomial and q-series identities. },
journal = {ArXiv e-prints (submitted)},
pages = {1--11},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {11},
url = {https://arxiv.org/abs/1903.01157}
}

@article{RISC5791,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Elementary Polynomial Identities Involving q-Trinomial Coefficients }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {0},
url = {https://arxiv.org/abs/1810.06497}
}

@article{RISC5736,
author = {J. Middeke and C.~Schneider},
title = {{Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems}},
language = {english},
journal = {To appear in ACM Communications in Computer Algebra},
pages = {--},
isbn_issn = {ISSN 1932-2240},
year = {2018},
note = {Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18)},
refereed = {yes},
length = {0}
}

@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}
}

@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}
}

@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}
}

@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}
}

@article{RISC5270,
author = {C. Schneider},
title = {{Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects}},
language = {english},
journal = {J. Symb. Comput.},
volume = {80},
number = {3},
pages = {616--664},
isbn_issn = {ISSN 0747-7171},
year = {2017},
note = {arXiv:1603.04285 [cs.SC]},
refereed = {yes},
length = {54},
url = {http://arxiv.org/abs/1603.04285}
}

@article{RISC5318,
author = {C. Schneider and R. Sulzgruber},
title = {{Asymptotic and exact results on the complexity of the Novelli--Pak--Stoyanovskii algorithm}},
language = {english},
journal = {Electron. J. Combin. },
volume = {24},
number = {2},
pages = {1--33},
isbn_issn = {ISSN: 1077-8926},
year = {2017},
note = {#P2.28, arXiv:1606.07597},
refereed = {yes},
length = {25},
url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p28}
}

@article{RISC5402,
author = {J. Blümlein and C. Schneider},
title = {{The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory}},
language = {english},
journal = {Physics Letters B},
volume = {771},
pages = {31--36},
isbn_issn = {ISSN 0370-2693},
year = {2017},
note = {arXiv:1701.04614 [hep-ph]},
refereed = {yes},
length = {6},
url = {https://doi.org/10.1016/j.physletb.2017.05.001}
}

@article{RISC5449,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},
title = {{The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,\rm N_F)}$}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {922},
pages = {1--40},
isbn_issn = {ISSN 0550-3213.},
year = {2017},
note = {arXiv:1705.01508 [hep-ph]},
refereed = {yes},
length = {40},
url = {https://arxiv.org/abs/1705.01508}
}