example sum

Evaluation of Feynman Integrals:


  1. J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, C. Schneider, F. Wißbrock Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses. To appear in Nucl. Phys. B., pp. 1-99. 2017. ISSN 0550-3213. arXiv:1705.07030 [hep-ph]. [url] [bib]

  2. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, \rm N_F)}$. To appear in Nucl. Phys. B., pp. 1-38. 2017. ISSN 0550-3213.. arXiv:1705.01508 [hep-ph]. [url] [bib]

  3. A. Behring, J. Blümlein, G. Falcioni, A. De Freitas, A. von Manteuffel, C. Schneider The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^+-W^-}(x, Q^2)$ and $F_2^{W^+-W^-}(x, Q^2)$. Physical Review D 94(11), pp. 1-19. 2016. ISSN 1550-2368. arXiv:1609.06255 [hep-ph]. [url] [bib]

  4. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wißbrock, Heavy flavour corrections to polarised and unpolarised deep-inelastic scattering at 3-loop order. In: Proceedings of the QCD Evolution 2016, PoS(QCDEV2016)052, pp. 1-16. 2016. National Institute for Subatomic Physics (Nikhef) in Amsterdam, ISSN 1824-8039. arXiv:1611.01104 [hep-ph]. [url] [bib]

  5. J. Ablinger, J. Behring, J. Blümlein, G. Falcioni, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering. In: Proc. Loops and Legs in Quantum Field Theory - LL 2016, J. Bluemlein and P. Marquard and T. Riemann (ed.), Proc. of Sciences PoS (LL2016) 065, pp. 1-16. 2016. ISSN 1824-8039. arXiv:1609.03397 [hep-ph]. [url] [bib]

  6. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra. Comput. Phys. Comm. 202, pp. 33-112. 2016. ISSN 0010-4655. arXiv:1509.08324 [hep-ph]. [url] [bib]

  7. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C.G. Raab, M. Round, C. Schneider, F. Wißbrock 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. In: Proceedings of EPS 2015, , pp. 1-13. 2016. ISSN 1824-8039. [url] [bib]

  8. A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Schneider. The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x, Q^2) at Large Momentum Transfer. Physical Review D 92(114005), pp. 1-19. 2015. ISSN 1550-2368. arXiv:1508.01449 [hep-ph]. [url] [bib]

  9. A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x, Q^2) at Large Momentum Transfer. Nucl. Phys. B 897, pp. 612-644, 2015. ISSN 0550-3213.. arXiv:1504.08217 [hep-ph]. [url] [bib]

  10. J. Blümlein, A. De Freitas, C. Schneider Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering. In: Advances in Computational Particle Physics, J. Blümlein, K. Jansen, M. Krämer, J.H. Kühn (ed.), Proceedings of Final Meeting of DFG SFB-TR-9, Nucl. Phys. B (Proc. Suppl.) , pp. 185-201. 2015. ISSN 0550-3213. arXiv:1411.5669 [hep-ph]. [url] [bib]

  11. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, S. Schneider, F. Wißbrock 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering. 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] [bib]

  12. J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider 3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$. In: 17th International Conference in Quantum Chromodynamics (QCD 14), Stephan Narison (ed.), Proceedings of QCD Montpellier Conference, Nucl. Phys. B (Proc. Suppl.) 258-259, pp. 37-40. 2015. ISSN 0550-3213. arXiv:1409.1435 [hep-ph]. [url] [bib]

  13. J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x, Q^2)$ and the Anomalous Dimension. Nuclear Physics B 890, pp. 48-151. 2015. ISSN 0550-3213. arXiv:1409.1135 [hep-ph]. [url] [bib]

  14. A. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wißbrock Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering. 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] [bib]

  15. J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wißbrock 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines. In: Proceedings of Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)015 , pp. 1-10. 2014. ISSN 1824-8039. arXiv:1407.2821 [hep-ph]. [url] [bib]

  16. J. Blümlein, I. Dubovyk, J. Gluza, M. Ochman, C.G. Raab, T. Riemann, C. Schneider. Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)52 , pp. 1-14. 2014. [url] [bib]

  17. J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for thE Structure Function \boldmath $F_2(x, Q^2)$ and Transversity. Nuclear Physics B 886, pp. 733-823. 2014. arXiv:1406.4654 [hep-ph]. [url] [bib]

  18. J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider The $O(\alpha_s^3 T_F^2)$ Contributions to the Gluonic Operator Matrix Element. Nuclear Physics B 885, pp. 280-317. 2014. ISSN: 0550-3213. arXiv:1405.4259 [hep-ph]. [url] [bib]

  19. J. Ablinger, J. Blümlein, C. Raab, C. Schneider, F. Wissbrock Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms. Nuclear Physics B 885, pp. 409-447. 2014. ISSN: 0550-3213. arXiv:1403.1137 [hep-ph]. [url] [bib]

  20. J. Ablinger, J. Bluemlein, A. De Freitas A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock The Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O(\alpha_s^3)$. Nuclear Physics B 882, pp. 263-288. 2014. ISSN: 0550-3213. arXiv:1402.0359 [hep-ph]. [url] [bib]

  21. A. Behring, J. Bluemlein, A. De Freitas, T. Pfoh, C. Raab, M. Round, J. Ablinger, A. Hasselhuhn, C. Schneider, F. Wissbrock, A. von Manteuffel New Results on the 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering. In: Proc. of RADCOR, , PoS(RADCOR 2013)058 , pp. 1-21. 2013. ISSN 1824-8039. arXiv:1312.0124 [hep-ph]. [url] [bib]

  22. J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wissbrock Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. 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] [bib]

  23. J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider The $O(α_s^3 n_f T_F^2 C_{A, F})$} Contributions to the Gluonic Massive Operator Matrix Elements. Nuclear Physics B(866), pp. 196-211. 2013. [url] [pdf] [bib]

  24. J. Bluemlein, T. Riemann, C. Schneider Precision Calculations, Algebraic Summation and Integration - Towards the Mathematical Structure of the Microcosm. In: Annual report 2012 of the particle and astroparticle physics division at DESY, - (ed.), pp. 90-91. 2013. Deutsches Elektronen Synchrotron (DESY). [url] [bib]

  25. J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock New Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. Proceedings of the 36th International Conference on High Energy Physics, PoS(ICHEP2012)270, pp. 1-9. 2012. [url] [bib]

  26. J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, S. Klein, C. Raab, M. Round, C. Schneider, F. Wissbrock Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N. In: Proc. Loops and Legs in Quantum Field Theory 2012, J. Bl[mlein, S. Moch, T. Riemann (ed.), PoS(LL2012)033 , pp. 1-12. 2012. [url] [bib]

  27. J. Ablinger, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements. Nuclear Physics B. 864 (2012), pp. 52-84 [url] [bib]

  28. J. Ablinger, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock New Heavy Flavor Contributions to the DIS Structure Function $F_2(x, Q^2)$ at $O(\alpha_s^3)$. In: Proceedings of RADCOR 2011, , Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) PoS(RADCOR2011)31, pp. 1-8. 2011.  [url] [bib]

  29. J. Ablinger, J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines. To appear in Proc. of 19th International Workshop On Deep-Inelastic Scattering And Related Subjects (DIS 2011). [url] [bib]

  30. J. Ablinger,  J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. The O(\alpha_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x, Q^2) and Transversity. Nucl. Phys. B, 844, pp. 26-54. 2011. [url] [bib]

  31. J. Ablinger, I. Bierenbaum, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock. Heavy Flavor DIS Wilson coefficients in the asymptotic regime. Nucl. Phys. B (Proc. Suppl.) 205-206 (2010), pp 242-249. arXiv::1007.0375 [hep-ph]. [url] [bib]

  32. J. Ablinger, J. Bluemlein, S. Klein, C. Schneider. Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams . Nucl. Phys. B (Proc. Suppl.) 205-206 (2010), pp 110-115. arXiv::1006.4797 [math-ph]. [url] [bib]

  33. Flavia Stan. On Recurrences for Ising Integrals. Adv. in Appl. Math. 45(3), pp. 334-345. 2010. [pdf] [bib]

  34. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. [pdf] [bib]

  35. Bierenbaum, J. Bluemlein, S. Klein, C. Schneider. Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(epsilon)$. Nucl.Phys. B 803(1-2), pp. 1-41. November 2008. [url] [pdf] [bib]

  36. J. Bluemlein, M. Kauers, S. Klein, C. Schneider. From Moments to Functions in Quantum Chromodynamics. In Proc. ACAT 2008, PoS(ACAT08)106. [ps] [pdf] [bib]

  37. S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007PoS(ACAT)083, pp. 1-11. 2007. [url] [pdf] [bib]

  38. I. Bierenbaum, J. Blümlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007 PoS(ACAT)082, pp. 1-15. 2007. [url] [pdf] [bib]



Special functions:


  1. J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C.G. Raab, C.-S. Radu, C. Schneider Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams. submitted, pp. 1-68. 2017. arXiv:1706.01299 [hep-th]. [url] [bib]

  2. J. Ablinger Discovering and Proving Infinite Binomial Sums Identities. Experimental Mathematics 26(1), pp. 62-71. 2017. ISSN 1058-6458. 10.1080/10586458.2015.1116028. [url] [bib]

  3. J. Ablinger Inverse Mellin Transform of Holonomic Sequences. In: Proc. Loops and Legs in Quantum Field Theory - LL 2016, J. Bluemlein and P. Marquard and T. Riemann (ed.), Proc. of Sciences PoS (LL2016) 067, pp. -. 2016. ISSN 1824-8039. arXiv:1606.02845 [cs.SC]. [url] [bib]J.

  4. J. Ablinger, C. Schneider. Algebraic independence of (cyclotomic) harmonic sums, submitted, 2015. arXiv:1510.03692 [cs.SC]. [url] [bib]

  5. J. Ablinger, J. Blümlein, C G. Raab, C. Schneider. Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)020 , pp. 1-13. 2014. arXiv:1407.4721 [hep-th]. [url] [bib]

  6. J. Ablinger The package HarmonicSums: Computer Algebra and Analytic aspects of Nested Sums. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), pp. 1-10. 2014. ISSN 1824-8039. [bib]

  7. J. Ablinger, J. Blümlein, C.G. Raab, C. Schneider. Iterated Binomial Sums and their Associated Iterated Integrals. J. Math. Phys. 55(112301), pp. 1-57. 2014. ISSN 0022-2488. arXiv:1407.1822 [hep-th]. [url] [bib]

  8. J. Ablinger, J. Bluemlein, C. Schneider Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers. In: Proc. ACAT 2013, , J. Phys.: Conf. Ser 523/012060, pp. 1-10. 2014. ISSN 1742-6596. arXiv:1310.5645 [math-ph]. [url] [bib]

  9. S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann. Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC]. [url] [bib]

  10. J. Ablinger, J. Bluemlein, C. Schneider. Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms. J. Math. Phys. 54, 082301 (2013); 54(082301), pp. 1-74. 2013. arXiv:1302.0378 [math-ph]. [url] [pdf] [bib]

  11. J. Ablinger, J. Bluemlein. Harmonic Sums, Polylogarithms, Special Numbers, and their Generalizations. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, J. Bluemlein, C. Schneider (ed.), Texts and Monographs in Symbolic Computation , pp. 1-31. 2013. Springer. [url] [bib]

  12. J. Ablinger Computer Algebra Algorithms for Special Functions in Particle Physics. J. Kepler University Linz. PhD Thesis. April 2012. [pdf] [bib]

  13. J. Ablinger, J. Bluemlein, C. Schneider Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. J. Math. Phys. 52(10), pp. 1-52. 2011.  [arXiv:1007.0375 [hep-ph]]. [url] [pdf] [bib]

  14. C. Schneider. Parameterized Telescoping Proves Algebraic Independence of Sums. Ann. Comb. 14(4), pp. 533-552. 2010. [pdf] [bib]

  15. M. Kuba, H. Prodinger, C. Schneider. Generalized Reciprocity Laws for Sums of Harmonic Numbers. INTEGERS. Electronic Journal of Combinatorial Number Theory 8(A17), pp. 1-20. 2008.  [url] [pdf] [bib]

  16. Jakob Ablinger A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics. Johannes Kepler University. Diploma Thesis. February 2009. [pdf] [bib]


Computer algebra - Symbolic summation and integration:


  1. J. Blümlein, M. Round, C. Schneider Refined Holonomic Summation Algorithms in Particle Physics. In: submitted pp. 1-39. 2017. arXiv:1706.03677 [cs.SC]. [url] [bib]

  2. E.D. Ocansey, C. Schneider Representing (q-)hypergeometric products and mixed versions in difference rings. submitted, , pp. 1-36. 2017. arXiv:1705.01368 [cs.SC]. [url] [bib]

  3. J. Middeke, C. Schneider Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions. Submitted, , pp. 1-24. 2017. arXiv:1705.00280 [cs.SC]. [url] [bib]

  4. J. Blümlein, C. Schneider The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory. Physics Letters B 771, pp. 31-36. 2017. arXiv:1701.04614 [hep-ph]. [url] [bib]

  5. C. Schneider Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects. J. Symb. Comput. 80(3), pp. 616-664. 2017. ISSN 0747-7171. arXiv:1603.04285 [cs.SC]. [url] [bib]

  6. E.D. Ocansey, C. Schneider Representation of hypergeometric products in difference rings. ACM Communications in Computer Algebra 50(4), pp. 161-163. 2016. ISSN 1932-2240 . Extended abstract of the poster presentation at ISSAC 2016. [pdf] [bib]

  7. J. Middeke, C. Schneider Denominator Bounds for Higher Order Systems of Linear Recurrence Equations. ACM Communications in Computer Algebra 50(4), pp. 185-187. 2016. ISSN 1932-2240. Extended abstract of the poster presentation at ISSAC 2016. [pdf] [bib]

  8. J. Ablinger, A. Behring, J. Bluemlein, A. de Freitas, C. Schneider Algorithms to solve coupled systems of differential equations in terms of power series. In: Proc. Loops and Legs in Quantum Field Theory - LL 2016, J. Bluemlein, P. Marquard, T. Riemann (ed.) (ed.)PoS(LL2016)005, pp. 1-15. 2016. ISSN 1824-8039. arXiv:1608.05376 [cs.SC]. [url] [bib]

  9. C. Schneider Symbolic Summation in Difference Rings and Applications. In: Proc. ISSAC 2016, M. Rosenkranz (ed.), pp. 9-12. 2016. ISBN 978-1-4503-4380-0/16/07. [pdf] [bib]

  10. C. Schneider A Difference Ring Theory for Symbolic Summation. J. Symb. Comput. 72, pp. 82-127. 2016. arXiv:1408.2776 [cs.SC]. [url] [bib]

  11. C. Schneider Fast Algorithms for Refined Parameterized Telescoping in Difference Fields. In: Computer Algebra and Polynomials, Applications of Algebra and Number Theory, Jaime Gutierrez, Josef Schicho, Martin Weimann (ed.), Lecture Notes in Computer Science (LNCS) , pp. 157-191. 2015. Springer, ISSN: 0302-9743 . arXiv:1307.7887 [cs.SC]. [url] [bib]

  12. C. Schneider A streamlined difference ring theory: Indefinite nested sums, the alternating sign and the parameterized telescoping problem. In: Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 15th International Symposium, Franz Winkler, Viorel Negru, Tetsuo Ida, Tudor Jebelean, Dana Petcu, Stephen Watt, Daniela Zaharie (ed.), pp. 26-33. 2014. IEEE Computer Society, ISBN-13:978-1-4799-8448-0. arXiv:1412.2782v1 [cs.SC]. [url] [bib]

  13. A. De Freitas, J. Blümlein, C. Schneider Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)017, pp. 1-13. 2014. ISSN 1824-8039. [url] [bib]

  14. C. Schneider Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction. In: Proc. ACAT 2013, , J. Phys.: Conf. Ser. 523/012037, pp. 1-17. 2014. ISSN 1742-6596. arXiv:1310.0160 [cs.SC]. [url] [bib]

  15. C. Schneider Symbolic Summation in Difference Fields and Its Application in Particle Physics. Computer Algebra Rundbrief 53, pp. 8-12. 2013. ISSN 0933-5994. [url] [bib]

  16. C. Schneider, J. Bluemlein (ed.) Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions. Texts and Monographs in Symbolic Computation, 2013. Springer Wien, [bib]

  17. J. Ablinger, J. Bluemlein, M. Round, C. Schneider. Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals. In: Loops and Legs in Quantum Field Theory 2012 PoS(2012) , pp. 1-14. 2012.  [url] [bib]

  18. J. Bluemlein, S. Klein, C. Schneider, F. Stan A Symbolic Summation Approach to Feynman Integral Calculus. J. Symbolic Comput. 47, pp 1267-1289, 2012.  [pdf] [bib]

  19. M. Kauers, C. Schneider. A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations. In: Proc. of ISSAC 2011, Anton Leykin (ed.), pp. 201-208. 2011.  [pdf] [ps] [bib]

  20. J. Bluemlein, A. Hasselhuhn, C. Schneider Evaluation of Multi-Sums for Large Scale Problems. In: Proceedings of RADCOR 2011, , Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)PoS(RADCOR2011)32, pp. 1-9. 2012. [url] [bib]

  21. Burcin Erocal Algebraic extensions for summation in finite terms. RISC, Johannes Kepler University, Linz. PhD Thesis. February 2011. [pdf] [bib]

  22. B. Erocal and A. Storjohann. Nullspace computation over rational function fields for symbolic summation. Poster presentation at ISSAC 2010. Also appeared in ACM Communications in Computer Algebra, Vol. 44, No. 3, September 2010. [pdf] [bib]

  23. M. Kauers, C. Schneider. Partial Denominator Bounds for Partial Linear Difference Equations. In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 211-218.2010. [pdf] [ps] [bib]

  24. C. Schneider. Structural Theorems for Symbolic Summation. Appl. Algebra Engrg. Comm. Comput. 21(1), pp. 1-32. 2010. [pdf] [bib]

  25. C. Schneider. A symbolic summation approach to find optimal nested sum representations. In: Motives, Quantum Field Theory, and Pseudodifferential Operators, A. Carey, D. Ellwood, S. Paycha, S. Rosenberg (ed.), Clay Mathematics Proceedings 12, pp. 285-308. 2010. Amer. Math. Soc. [pdf] [bib]

  26. Flavia Stan. Algorithms for Special Functions: Computer Algebra and Analytical Aspects. RISC, Johannes Kepler University Linz. PhD Thesis. June 2010. RISC technical report 10-19. [pdf] [bib]

  27. Karen T. Kohl and Flavia Stan. An Algorithmic Approach to the Mellin Transform Method. In: Gems in Experimental Mathematics, T. Amdeberhan, L. A. Medina, V. H. Moll (ed.), Contemporary Mathematics 517, pp. 207-218. 2010. AMS, ISBN 978-0-8218-4869-2. [pdf] [bib]

  28. J. Bluemlein, S. Klein, C. Schneider, F. Stan. A symbolic summation approach to Feynman integrals. Poster presentation at ISSAC 2010. Also appeared in ACM SIGSAM Bulletin 44(3/4), pp. 95-96. 2010. [pdf] [bib]

  29. Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler. Algorithms in Symbolic Computation. In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [bib]

  30. C. Schneider. A Refined Difference Field Theory for Symbolic Summation. J. Symbolic Comput. 43(9), pp. 611-644. 2008. [pdf] [bib]

  31. C. Schneider. Simplifying Sums in PiSigma-Extensions. J. Algebra Appl. 6(3), pp. 415-441. 2007. [ps] [pdf] [bib]

  32. M. Kauers, C. Schneider. Symbolic Summation with Radical Expressions. In: Proc. ISSAC'07, C. W. Brown (ed.), pp. 219-226. 2007. ACM Press  [pdf] [ps] [bib]

  33. C. Schneider. Parameterized telescoping proves algebraic independence of sums. 2007. Poster presentation at FPSAC 2007. [url] [pdf] [pdf] [bib]

  34.  M. Kauers, C. Schneider. Indefinite Summation with Unspecified Summands. Discrete Math., 306(17), pp. 2073-2083. 2006. Preliminary version online. [pdf] [bib]

  35. M. Kauers, C. Schneider. Application of Unspecified Sequences in Symbolic Summation. In: Proc. ISSAC'06, Jean-Guillaume Dumas (ed.) pp. 177-183. 2006. ACM Press, [ps] [pdf] [bib]

  36.  C. Schneider. Product Representations in PiSigma-Fields. Annals of Combinatorics, 9(1), pp. 75-99. 2005. Preliminary version online. [pdf] [ps] [bib]

  37. C. Schneider. A new Sigma approach to multi-summation. Advances in Applied Math., Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud, 34(4), pp. 740-767. 2005. Preliminary version online. [ps] [pdf] [bib]

  38. C. Schneider. Degree Bounds To Find Polynomial Solutions of Parameterized Linear Difference Equations in PiSigma-Fields. Appl. Algebra Engrg. Comm. Comput., 16(1), pp. 1-32. 2005. Preliminary version online. [pdf] [ps] [bib]

  39. C. Schneider. Solving Parameterized Linear Difference Equations in Terms of Indefinite Nested Sums and Products.J. Differ. Equations Appl., 11(9), pp. 799-821. 2005. Preliminary version online. [pdf] [ps] [bib]

  40. C. Schneider. Finding Telescopers with Minimal Depth for Indefinite Nested Sum and Product Expressions. In: Proc. ISSAC'05, M. Kauers (ed.), pp. 285-292. 2005. ACM Press. [pdf] [ps] [bib]

  41. C. Schneider. Symbolic Summation with Single-Nested Sum Extensions. In: Proc. ISSAC'04, J. Gutierrez (ed.), pp. 282-289. 2004. ACM Press. [pdf] [ps] [bib]

  42. C. Schneider. A Collection of Denominator Bounds to Solve Parameterized Linear Difference Equations in PiSigma-Extensions. An. Univ. Timisoara Ser. Mat.-Inform., 42(2), pp. 163-179. 2004 .Extended version of Proc. SYNASC'04; preliminary version online. [pdf] [ps] [bib]

  43. C. Schneider. Symbolic Summation in Difference Fields. RISC, J. Kepler University Linz. PhD Thesis (advisor P. Paule). May 2001. (published as Technical report no. 01-17 in RISC Report Series). [pdf][ps] [bib]

  44. C. Schneider. An Implementation of Karr's Summation Algorithm in Mathematica. Sem. Lothar. Combin. S43b, pp. 1-10. 2000. [url] [pdf] [ps] [bib]



Related publications (combinatorics, number theory, ...):



  1. C. Krattenthaler, C. Schneider Evaluation of binomial double sums involving absolute values. submitted, pp. 1-36. 2016. arXiv:1607.05314 [math.CO]. [url] [bib]

  2. C. Schneider, R. Sulzgruber Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm. Electron. J. Combin. 24(2), pp. 1-33. 2017. #P2.28, arXiv:1606.07597. [url] [bib]

  3. H. Prodinger, C. Schneider, S. Wagner. Unfair permutations. Europ. J. Comb. 32, pp. 1282-1298. 2011. [pdf] [bib]

  4. C. Schneider, R. Osburn. Gaussian Hypergeometric series and supercongruences. Math. Comp. 78(275-292), pp. 1-19. 2009. [url] [pdf] [bib]

  5. Flavia Stan Computer-Assisted Proofs of Special Function Identities Related to Poisson Integrals. The Ramanujan Journal 20(1), pp. 55-67. 2009. Springer,  [pdf] [bib]

  6. Manuel Kauers , Carsten Schneider. Automated Proofs for Some Stirling Number Identities. The Electronic Journal of Combinatorics 15(1), pp. 1-7. 2008. [pdf] [ps] [bib]

  7. S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann. Computing the complexity for schelling segregation models. Communications in Nonlinear Science and Numerical Simulations 13, pp. 2236-2245. 2008. [pdf] [bib]

  8. P. Paule, C. Schneider. Truncating Binomial Series with Symbolic Summation. INTEGERS. Electronic Journal of Combinatorial Number Theory(7), #A22., pp. 1-9. 2007.  [url] [pdf] [bib]

  9. C. Schneider, R. Pemantle. When is 0.999... equal to 1?. Amer. Math. Monthly, 114(4), pp. 344-350. 2007. Preliminary version online. [ps] [pdf] [bib]

  10. C. Schneider. Apery's Double Sum is Plain Sailing Indeed. Electron. J. Combin., 14, #N5, pp. 1-3. 2007. [url] [pdf] [ps] [bib]

  11. C. Schneider. Symbolic Summation Assists Combinatorics. Sem. Lothar. Combin., 56, Article B56b, pp. 1-36. 2007. [url] [pdf] [ps] [bib]

  12. A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, J. Schoeberl. Hypergeometric Summation Algorithms for High Order Finite Elements. Computing, 78(3), pp. 235-249. 2006. Preliminary version available. [pdf] [ps] [bib]

  13. K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e Approximations to the Logarithm II: Identities, Recurrences, and Symbolic Computation. Ramanujan Journal, 11(2), pp. 139-158. 2006. Preliminary version online. [url] [pdf] [ps] [bib]

  14. K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e Approximations to the Logarithm III: Alternative Methods and Additional Results. Ramanujan Journal, 12(3), pp. 299-314. 2006. Preliminary version online. [pdf] [ps] [ps] [bib]

  15. C. Schneider. Some Notes On ``When is 0.999... equal to 1?''. In: Mathematics, Algorithms, Proofs, T. Coquand et al. (ed.), Dagstuhl Seminar Proceedings 05021, pp. 1-3. 2006. Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany. [url] [pdf] [bib]

  16. G. E. Andrews, P. Paule, C. Schneider. Plane Partitions VI: Stembridge's TSPP Theorem. Advances in Applied Math., Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud, 34(4), pp. 709-739. 2005. Preliminary version online. [ps] [pdf] [bib]

  17. C. Schneider. The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application. Discrete Math. Theor. Comput. Sci., 6(2), pp. 365-386. 2004. [url][pdf] [ps] [bib]

  18. P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math., 31(2), pp. 359-378. 2003. Preliminary version online. [pdf][ps] [bib]

  19. P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math., 31(2), pp. 359-378. 2003. Preliminary version online. [pdf][ps] [bib]

  20. C. Schneider. How one can play with sums. In: Proceedings of the 8th Rhine Workshop on Computer Algebra, H. Kredel, W. Seiler (ed.), pp. 73-83. 2002. Mannheim, Germany. Preliminary version online. [pdf] [ps] [bib]



Theses (in this group or related to the DESY cooperation):




  1. A. Behring (DESY)     
    Three-loop QCD corrections from massive quarks to deep-inelastic structure functions and operator matrix elements
    (Hasylab, DESY). 2016. 326 pp. DOI: 10.3204/PUBDB-2016-05723

  2. F.P. Wißbrock (DESY)    
    O(α3s) contributions to the heavy flavor Wilson coefficients of the structure function F2(x,Q2) at Q2≫m2
    (Dortmund U. & DESY, Zeuthen). 2015. 214 pp. DESY-THESIS-2015-040

  3. A. Hasselhuhn (DESY)
    3-Loop Contributions to Heavy Flavor Wilson Coefficients of Neutral and Charged Current DIS
    (Tech. U., Dortmund (main) & DESY, Zeuthen & Linz U.). 2013. 187 pp. DESY-THESIS-2013-050

  4. J. Ablinger (RISC)
    Computer Algebra Algorithms for Special Functions in Particle Physics. Johannes Kepler University Linz. PhD-Thesis. April 2012. [pdf]

  5.  B. Erocal (RISC)
    Algebraic extensions for summation in finite terms. RISC, Johannes Kepler Universitz Liny. PHD-Thesis. February 2011.
    [pdf] [bib]

  6. F. Stan (RISC)
    Algorithms for Special Functions: Computer Algebra and Analytical Aspects. Johannes Kepler University Linz. PhD-Thesis. July 2010. [pdf]

  7. F. Wißbrock (DESY)
    O(αs3 TF2 NF) Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function F2(x,Q2) at Q2 >> m2. Free University Berlin. Diploma Thesis. June 2010. arxiv:1010.4251 [hep-ph]. [pdf]

  8. S. Klein (DESY)
    Mellin Moments of Heavy Flavor Contributions to F2(x,Q2) at NNLO. Dortmund University. PhD-Thesis. September 2009. arxiv:0910.3101 [hep-ph]. [pdf]


  9. J. Ablinger (RISC)
    A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics. Johannes Kepler University Linz. Diploma Thesis. February 2009. arXiv:1011.1176 [math-ph]. [pdf]