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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 523012060, pp. 1-10. 2014. ISSN 1742-6596. arXiv:1310.5645 [math-ph]. [url] [bib]
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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. 2014. ISSN 1824-8039. arXiv:1312.0124 [hep-ph]. [url] [bib]
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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]
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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]
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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]
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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 $F_2(x, Q^2)$ and Transversity. Nuclear Physics B 886, pp. 733-823. 2014. ISSN: 0550-3213. arXiv:1406.4654 [hep-ph]. [url] [bib]
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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]
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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. arXiv:1407.2537 [cs.SC]. [url] [bib]
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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]
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J. 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]
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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. ISSN 1824-8039. arXiv:1407.4721 [hep-th]. [url] [bib]
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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. ISSN 1824-8039. arXiv:1407.7832 [hep-ph]. [url] [bib]
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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] [pdf] [bib]
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C. Schneider. Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages {S}igma, {EvaluateMultiSums} and {SumProduction}. In: Proc. ACAT 2013, - (ed.), J. Phys.: Conf. Ser. 523, pp. 1-17. 2014. ISSN 1742-6596. arXiv:1310.0160 [cs.SC]. [url] [bib]
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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. ISSN: 0550-3213. arXiv:1205.4184 [hep-ph]. [url] [pdf] [bib]
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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. In: Proceedings of the 36th International Conference on High Energy Physics, PoS(ICHEP2012)270, pp. 1-9. 2013. ISSN 1824-8039. arXiv:1212.5950 [hep-ph]. [url] [bib]
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J. Ablinger, J. Bluemlein, C. Schneider. Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms. J. Math. Phys. 54(082301), pp. 1-74. 2013. ISSN 0022-2488. arXiv:1302.0378 [math-ph]. [url] [pdf] [bib]
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C. Schneider. Simplifying Multiple Sums in Difference Fields. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 325-360. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1304.4134 [cs.SC]. [url] [pdf] [bib]
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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]
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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] [pdf] [bib]
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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]
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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]
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J. Bluemlein, S. Klein, C. Schneider, F. Stan. A Symbolic Summation Approach to Feynman Integral Calculus. J. Symbolic Comput. 47, pp. 1267-1289. 2012. ISSN 0747-7171. arXiv:1011.2656 [cs.SC]. [url] [pdf] [bib]
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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. 2012. ISSN 1824-8039. arXiv:1202.2700 [hep-ph]. [url] [bib]
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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. ISSN 1824-8039. arXiv:1202.4303 [math-ph]. [url] [bib]
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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, pp. 52-84. 2012. ISSN: 0550-3213. arXiv:1206.2252v1 [hep-ph]. [url] [pdf] [bib]
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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, J. Bluemlein, S. Moch, T. Riemann (ed.), PoS(LL2012) 50, pp. 1-14. 2012. ISSN 1824-8039. arXiv:1210.1685 [cs.SC]. [url] [bib]
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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. Blümlein, S. Moch, T. Riemann (ed.), PoS(LL2012)033 , pp. 1-12. 2012. ISSN 1824-8039. arXiv:1212.6823 [hep-ph]. [url] [bib]
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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. ISSN: 0550-3213. arXiv:1008.3347 [hep-ph]. [url] [bib]
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Manuel Kauers, Carsten Schneider. A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations. In: Proceedings of ISSAC 2011, Anton Leykin (ed.), pp. 201-208. 2011. 978-1-4503-0675-1. arXiv:1101.2803 [cs.SC]. [url] [pdf] [bib]
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H. Prodinger, C. Schneider, S. Wagner. Unfair permutations. Europ. J. Comb. 32, pp. 1282-1298. 2011. ISSN: 0195-6698. [url] [pdf] [bib]
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J. Ablinger, J. Bluemlein, C. Schneider. Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. J. Math. Phys. 52(10), pp. 1-52. 2011. ISSN 0022-2488 . arXiv:1105.6063 [math-ph]. [url] [pdf] [bib]
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J. Ablinger, J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines. In: 19th International Workshop On Deep-Inelastic Scattering And Related Subjects (DIS 2011), , pp. -. 2011. American Institute of Physics (AIP), [url] [bib]
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C. Schneider. Parameterized Telescoping Proves Algebraic Independence of Sums. Ann. Comb. 14(4), pp. 533-552. 2010. ISSN 0218-0006. arXiv:0808.2596. [url] [pdf] [bib]
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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, ISBN-10: 0-8218-5199-3. arXiv:0904.2323 . [url] [pdf] [bib]
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C. Schneider. Structural Theorems for Symbolic Summation. Appl. Algebra Engrg. Comm. Comput. 21(1), pp. 1-32. 2010. ISSN 0938-1279. [url] [pdf] [bib]
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Manuel Kauers, Carsten Schneider. Partial Denominator Bounds for Partial Linear Difference Equations. In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 211-218. 2010. 978-1-4503-0150-3. arXiv:1005.0602 [cs.SC]. [url] [ps] [pdf] [bib]
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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.), Loops and Legs in Quantum Field Theory - Proceedings of the 10th DESY Workshop on Elementary Particle Theory 205-206, pp. 110-115. 2010. ISSN 0550-3213. arXiv:1006.4797 [math-ph]. [url] [pdf] [bib]
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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.), Loops and Legs in Quantum Field Theory - Proceedings of the 10th DESY Workshop on Elementary Particle Theory 205-206, pp. 242-249. 2010. ISSN 0550-3213. arXiv::1007.0375 [hep-ph]. [url] [pdf] [bib]
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I. Bierenbaum, J. Bl�mlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)082, pp. 1-15. 2009. ISSN 18248039. arXiv:0707.4659 [math-ph]. [url] [pdf] [bib]
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S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)083, pp. 1-11. 2009. ISSN 18248039. [url] [pdf] [bib]
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C. Schneider, R. Osburn. Gaussian Hypergeometric series and supercongruences. Math. Comp. 78(265), pp. 275-292. 2009. ISSN 0025-5718. arXiv:math/0610281 [math.NT]. [url] [pdf] [bib]
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J. Bluemlein, M. Kauers, S. Klein, C. Schneider. From moments to functions in higher order QCD . In: XII Advanced Computing and Analysis Techniques in Physics Research, - (ed.)PoS(ACAT08)106, pp. 1-7. 2009. ISSN 1824-8039. arXiv:0902.4095 [hep-ph]. [url] [pdf] [bib]
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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. [url] [pdf] [bib]
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J. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and {W}ilson coefficients from {M}ellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. ISSN 0010-4655. arXiv:0902.4091 [hep-ph]. [url] [pdf] [bib]
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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. April 2006. ISSN 1382-4090. Preliminary version online. [url] [pdf] [ps] [bib]
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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. ISSN 1382-4090. Preliminary version online. [url] [ps] [pdf] [ps] [bib]
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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, ISSN 1862-4405. [url] [pdf] [bib]
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M. Kauers, C. Schneider. Indefinite summation with unspecified summands. Discrete Math. 306(17), pp. 2073-2083. 2006. ISSN 0012-365X. Preliminary version online. [url] [pdf] [bib]
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M. Kauers, C. Schneider. Application of unspecified sequences in symbolic summation. In: Proceedings of ISSAC'06, Jean-Guillaume Dumas (ed.), Proceedings of ISSAC'06, pp. 177-183. 2006. ACM Press, [url] [ps] [pdf] [bib]
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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. ISSN 0010-485X. Preliminary version available. [url] [pdf] [ps] [bib]
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P. Paule, V. Pillwein, C. Schneider, J. Schöberl. Hypergeometric Summation Techniques for High Order Finite Elements. In: PAMM, , Proceedings of GAMM Annual Meeting 2006 - Berlin61, pp. 689-690. 2006. Wiley InterScience, Weinheim, ISBN. [url] [bib]
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