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

### Project Lead

### Project Duration

01/03/2013 - 28/02/2021### Project URL

Go to Website## Partners

### The Austrian Science Fund (FWF)

## Publications

### 2018

### An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences

#### J. Ablinger

In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018, J. Blümlein and P. Marquard (ed.), PoS(LL2018) , pp. 1-10. 2018. ISSN 1824-8039. [url]@

author = {J. Ablinger},

title = {{An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences}},

booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018}},

language = {english},

series = {PoS(LL2018)},

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2018},

editor = {J. Blümlein and P. Marquard},

refereed = {yes},

length = {10},

url = {https://pos.sissa.it/303/063/pdf}

}

**inproceedings**{RISC5789,author = {J. Ablinger},

title = {{An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences}},

booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018}},

language = {english},

series = {PoS(LL2018)},

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2018},

editor = {J. Blümlein and P. Marquard},

refereed = {yes},

length = {10},

url = {https://pos.sissa.it/303/063/pdf}

}

### Elementary Polynomial Identities Involving q-Trinomial Coefficients

#### Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]@

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**{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}

}

### Refined q-Trinomial Coefficients and Two Infinite Hierarcies of q-Series Identities

#### Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (submitted), pp. 1-10. 2018. N/A. [url]@

author = {Ali Kemal Uncu and Alexander Berkovich},

title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarcies 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 hierarcies contains an identity which is equivalent to Capparelli's first Partition Theorem. },

journal = {ArXiv e-prints (submitted)},

pages = {1--10},

isbn_issn = {N/A},

year = {2018},

refereed = {yes},

length = {10},

url = {https://arxiv.org/abs/1810.12048}

}

**article**{RISC5801,author = {Ali Kemal Uncu and Alexander Berkovich},

title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarcies 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 hierarcies contains an identity which is equivalent to Capparelli's first Partition Theorem. },

journal = {ArXiv e-prints (submitted)},

pages = {1--10},

isbn_issn = {N/A},

year = {2018},

refereed = {yes},

length = {10},

url = {https://arxiv.org/abs/1810.12048}

}

### 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]@

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}

}

**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}

}

### Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems

#### J. Middeke, C. Schneider

To appear in ACM Communications in Computer Algebra, pp. -. 2018. ISSN 1932-2240. Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18). [pdf] [pdf]@

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**{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}

}

### 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]@

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**{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}

}

### 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]@

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}

}

**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}

}

### 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]@

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**{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}

}

### 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]@

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**{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}

}

### 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]@

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**{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}

}

### 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.@

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}

}

**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}

}

### 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]@

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}

}

**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}

}

### Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects

#### C. Schneider

J. Symb. Comput. 80(3), pp. 616-664. 2017. ISSN 0747-7171. arXiv:1603.04285 [cs.SC]. [url]@

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**{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}

}

### Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm

#### C. Schneider, R. Sulzgruber

Electron. J. Combin. 24(2), pp. 1-33. 2017. ISSN: 1077-8926. #P2.28, arXiv:1606.07597. [url]@

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**{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}

}

### The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory

#### J. Blümlein, C. Schneider

Physics Letters B 771, pp. 31-36. 2017. ISSN 0370-2693. arXiv:1701.04614 [hep-ph]. [url]@

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**{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}

}

### The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, \rm N_F)}$

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

Nucl. Phys. B. 922, pp. 1-40. 2017. ISSN 0550-3213.. arXiv:1705.01508 [hep-ph]. [url]@

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}

}

**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}

}

### The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization

#### J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald

Cornell University. Technical report no. arXiv:1710.04500 [hep-ph], 2017. [url]@

author = {J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},

title = {{The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization}},

language = {english},

number = {arXiv:1710.04500 [hep-ph]},

year = {2017},

institution = {Cornell University},

length = {5},

url = {https://arxiv.org/abs/1710.04500}

}

**techreport**{RISC5488,author = {J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},

title = {{The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization}},

language = {english},

number = {arXiv:1710.04500 [hep-ph]},

year = {2017},

institution = {Cornell University},

length = {5},

url = {https://arxiv.org/abs/1710.04500}

}

### Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

In: Proceedings of QCDEV2017, L. Gamberg, A. Prokudin, J.W. Qiu and A. Radyushkin (ed.)PoS(QCDEV2017)031 , pp. 1-10. 2017. ISSN 1824-8039. arXiv:1711.07957 [hep-ph]. [url]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},

title = {{Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results}},

booktitle = {{Proceedings of QCDEV2017}},

language = {english},

volume = {PoS(QCDEV2017)031 },

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.07957 [hep-ph]},

editor = {L. Gamberg and A. Prokudin and J.W. Qiu and A. Radyushkin},

refereed = {no},

length = {10},

url = {https://pos.sissa.it/308/}

}

**inproceedings**{RISC5506,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},

title = {{Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results}},

booktitle = {{Proceedings of QCDEV2017}},

language = {english},

volume = {PoS(QCDEV2017)031 },

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.07957 [hep-ph]},

editor = {L. Gamberg and A. Prokudin and J.W. Qiu and A. Radyushkin},

refereed = {no},

length = {10},

url = {https://pos.sissa.it/308/}

}

### The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

#### J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald, F. Wißbrock

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 071, pp. 1-20. 2017. ISSN 1824-8039. arXiv:1712.00745 [hep-ph]. [url]@

author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald and F. Wißbrock},

title = {{The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme}},

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

language = {english},

volume = {PoS (RADCOR2017) 071},

pages = {1--20},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = { arXiv:1712.00745 [hep-ph]},

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

refereed = {no},

length = {20},

url = {https://pos.sissa.it/290/071/pdf}

}

**inproceedings**{RISC5513,author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald and F. Wißbrock},

title = {{The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme}},

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

language = {english},

volume = {PoS (RADCOR2017) 071},

pages = {1--20},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = { arXiv:1712.00745 [hep-ph]},

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

refereed = {no},

length = {20},

url = {https://pos.sissa.it/290/071/pdf}

}

### Special functions, transcendentals and their numerics

#### Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten 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) 010, pp. 1-7. 2017. ISSN 1824-8039. arXiv:1712.08541 [hep-th]. [url]@

author = {Jakob Ablinger and Johannes Blümlein and Mark Round and Carsten Schneider},

title = {{Special functions, transcendentals and their numerics}},

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

language = {english},

volume = {PoS (RADCOR2017) 010},

pages = {1--7},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = { arXiv:1712.08541 [hep-th]},

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

refereed = {no},

length = {7},

url = {https://pos.sissa.it/290/010/pdf}

}

**inproceedings**{RISC5521,author = {Jakob Ablinger and Johannes Blümlein and Mark Round and Carsten Schneider},

title = {{Special functions, transcendentals and their numerics}},

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

language = {english},

volume = {PoS (RADCOR2017) 010},

pages = {1--7},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = { arXiv:1712.08541 [hep-th]},

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

refereed = {no},

length = {7},

url = {https://pos.sissa.it/290/010/pdf}

}