Kauers, Manuel; Koutschan, Christoph; Verron, Thibaut Transcendence certificates for D-finite functions. (English) Zbl 07760782 Dickenstein, Alicia (ed.) et al., Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24–27, 2023. New York, NY: Association for Computing Machinery (ACM). 372-380 (2023). MSC: 68W30 PDFBibTeX XMLCite \textit{M. Kauers} et al., in: Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24--27, 2023. New York, NY: Association for Computing Machinery (ACM). 372--380 (2023; Zbl 07760782) Full Text: DOI arXiv
Chen, Shaoshi; Du, Lixin; Kauers, Manuel Hermite reduction for D-finite functions via integral bases. (English) Zbl 07760758 Dickenstein, Alicia (ed.) et al., Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24–27, 2023. New York, NY: Association for Computing Machinery (ACM). 155-163 (2023). MSC: 68W30 PDFBibTeX XMLCite \textit{S. Chen} et al., in: Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24--27, 2023. New York, NY: Association for Computing Machinery (ACM). 155--163 (2023; Zbl 07760758) Full Text: DOI arXiv
Kauers, Manuel; Koutschan, Christoph Some D-finite and some possibly D-finite sequences in the OEIS. (English) Zbl 07732122 J. Integer Seq. 26, No. 4, Article 23.4.5, 42 p. (2023). MSC: 11B37 68W30 05A15 33C20 PDFBibTeX XMLCite \textit{M. Kauers} and \textit{C. Koutschan}, J. Integer Seq. 26, No. 4, Article 23.4.5, 42 p. (2023; Zbl 07732122) Full Text: arXiv Link
Buchacher, Manfred; Kauers, Manuel; Trotignon, Amélie Quadrant walks starting outside the quadrant. (English) Zbl 1505.05010 Sémin. Lothar. Comb. 85B, Article 26, 11 p. (2021). MSC: 05A15 PDFBibTeX XMLCite \textit{M. Buchacher} et al., Sémin. Lothar. Comb. 85B, Article 26, 11 p. (2021; Zbl 1505.05010) Full Text: arXiv Link
Buchacher, Manfred; Hofmanninger, Sophie; Kauers, Manuel Walks with small steps in the 4D-orthant. (English) Zbl 1460.05010 Ann. Comb. 25, No. 1, 153-166 (2021). MSC: 05A15 60G50 PDFBibTeX XMLCite \textit{M. Buchacher} et al., Ann. Comb. 25, No. 1, 153--166 (2021; Zbl 1460.05010) Full Text: DOI arXiv
Bacher, Axel; Kauers, Manuel; Yatchak, Rika Continued classification of 3D lattice models in the positive octant. (English. French summary) Zbl 1440.05017 Proceedings of the 28th international conference on formal power series and algebraic combinatorics, FPSAC 2016, Vancouver, Canada, July 4–8, 2016. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Math. Theor. Comput. Sci., Proc., 95-106 (2020). MSC: 05A15 05-08 60G50 PDFBibTeX XMLCite \textit{A. Bacher} et al., in: Proceedings of the 28th international conference on formal power series and algebraic combinatorics, FPSAC 2016, Vancouver, Canada, July 4--8, 2016. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 95--106 (2020; Zbl 1440.05017) Full Text: arXiv Link
Chen, Shaoshi; Kauers, Manuel; Li, Ziming; Zhang, Yi Apparent singularities of D-finite systems. (English) Zbl 1427.13036 J. Symb. Comput. 95, 217-237 (2019). Reviewer: Vladimir P. Kostov (Nice) MSC: 13P10 68W30 12H05 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Symb. Comput. 95, 217--237 (2019; Zbl 1427.13036) Full Text: DOI arXiv
Huang, Hui; Kauers, Manuel D-finite numbers. (English) Zbl 1432.34003 Int. J. Number Theory 14, No. 7, 1827-1848 (2018). MSC: 34A05 33E30 33F05 33F10 PDFBibTeX XMLCite \textit{H. Huang} and \textit{M. Kauers}, Int. J. Number Theory 14, No. 7, 1827--1848 (2018; Zbl 1432.34003) Full Text: DOI arXiv
Chen, Shaoshi; van Hoeij, Mark; Kauers, Manuel; Koutschan, Christoph Reduction-based creative telescoping for Fuchsian D-finite functions. (English) Zbl 1379.68363 J. Symb. Comput. 85, 108-127 (2018). MSC: 68W30 12H20 33F10 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Symb. Comput. 85, 108--127 (2018; Zbl 1379.68363) Full Text: DOI arXiv
Kauers, Manuel; Wang, Rong-Hua Lattice walks in the octant with infinite associated groups. (English) Zbl 1378.05008 Drmota, Michael (ed.) et al., Extended abstracts of the ninth European conference on combinatorics, graph theory and applications, EuroComb 2017, Vienna, Austria, August 28 – September 1, 2017. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 61, 703-709 (2017). MSC: 05A15 PDFBibTeX XMLCite \textit{M. Kauers} and \textit{R.-H. Wang}, Electron. Notes Discrete Math. 61, 703--709 (2017; Zbl 1378.05008) Full Text: DOI arXiv
Chen, Shaoshi; Kauers, Manuel Some open problems related to creative telescoping. (English) Zbl 1420.68242 J. Syst. Sci. Complex. 30, No. 1, 154-172 (2017). MSC: 68W30 33F10 PDFBibTeX XMLCite \textit{S. Chen} and \textit{M. Kauers}, J. Syst. Sci. Complex. 30, No. 1, 154--172 (2017; Zbl 1420.68242) Full Text: DOI arXiv
Bostan, Alin; Chyzak, Frédéric; van Hoeij, Mark; Kauers, Manuel; Pech, Lucien Hypergeometric expressions for generating functions of walks with small steps in the quarter plane. (English) Zbl 1352.05013 Eur. J. Comb. 61, 242-275 (2017). MSC: 05A15 33C05 PDFBibTeX XMLCite \textit{A. Bostan} et al., Eur. J. Comb. 61, 242--275 (2017; Zbl 1352.05013) Full Text: DOI arXiv
Bostan, Alin; Bousquet-Mélou, Mireille; Kauers, Manuel; Melczer, Stephen On 3-dimensional lattice walks confined to the positive octant. (English) Zbl 1354.05006 Ann. Comb. 20, No. 4, 661-704 (2016). MSC: 05A15 PDFBibTeX XMLCite \textit{A. Bostan} et al., Ann. Comb. 20, No. 4, 661--704 (2016; Zbl 1354.05006) Full Text: DOI arXiv
Drmota, Michael; Kauers, Manuel; Spiegelhofer, Lukas On a conjecture of Cusick concerning the sum of digits of \(n\) and \(n+t\). (English) Zbl 1372.11010 SIAM J. Discrete Math. 30, No. 2, 621-649 (2016). MSC: 11A63 05A16 11B50 11B65 PDFBibTeX XMLCite \textit{M. Drmota} et al., SIAM J. Discrete Math. 30, No. 2, 621--649 (2016; Zbl 1372.11010) Full Text: DOI arXiv
Chen, Shaoshi; Kauers, Manuel; Singer, Michael F. Desingularization of Ore operators. (English) Zbl 1348.68300 J. Symb. Comput. 74, 617-626 (2016). MSC: 68W30 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Symb. Comput. 74, 617--626 (2016; Zbl 1348.68300) Full Text: DOI arXiv
Gerhold, Stefan; Kauers, Manuel; Koutschan, Christoph; Paule, Peter; Schneider, Carsten; Zimmermann, Burkhard Computer-assisted proofs of some identities for Bessel functions of fractional order. (English) Zbl 1311.33003 Schneider, Carsten (ed.) et al., Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer (ISBN 978-3-7091-1615-9/hbk; 978-1-4614-8523-0/ebook). Texts and Monographs in Symbolic Computation, 75-96 (2013). MSC: 33C10 33E10 PDFBibTeX XMLCite \textit{S. Gerhold} et al., in: Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer. 75--96 (2013; Zbl 1311.33003) Full Text: DOI arXiv
Chen, Shaoshi; Kauers, Manuel Trading order for degree in creative telescoping. (English) Zbl 1241.33021 J. Symb. Comput. 47, No. 8, 968-995 (2012). MSC: 33F10 68W30 PDFBibTeX XMLCite \textit{S. Chen} and \textit{M. Kauers}, J. Symb. Comput. 47, No. 8, 968--995 (2012; Zbl 1241.33021) Full Text: DOI arXiv
Koutschan, Christoph; Kauers, Manuel; Zeilberger, Doron Proof of George Andrews’s and David Robbins’s \(q\)-TSPP conjecture. (English) Zbl 1255.05011 Proc. Natl. Acad. Sci. USA 108, No. 6, 2196-2199 (2011). MSC: 05A15 PDFBibTeX XMLCite \textit{C. Koutschan} et al., Proc. Natl. Acad. Sci. USA 108, No. 6, 2196--2199 (2011; Zbl 1255.05011) Full Text: DOI arXiv
Bostan, Alin; Kauers, Manuel; Van Hoeij, Mark The complete generating function for Gessel walks is algebraic. (English) Zbl 1206.05013 Proc. Am. Math. Soc. 138, No. 9, 3063-3078 (2010). MSC: 05A15 14N10 33F10 68W30 33C05 97N80 PDFBibTeX XMLCite \textit{A. Bostan} et al., Proc. Am. Math. Soc. 138, No. 9, 3063--3078 (2010; Zbl 1206.05013) Full Text: DOI arXiv Backlinks: MO
Kauers, Manuel; Koutschan, Christoph; Zeilberger, Doron Proof of Ira Gessel’s lattice path conjecture. (English) Zbl 1203.05010 Proc. Natl. Acad. Sci. USA 106, No. 28, 11502-11505 (2009). MSC: 05A15 68W30 PDFBibTeX XMLCite \textit{M. Kauers} et al., Proc. Natl. Acad. Sci. USA 106, No. 28, 11502--11505 (2009; Zbl 1203.05010) Full Text: DOI arXiv Link Backlinks: MO
Blümlein, Johannes; Kauers, Manuel; Klein, Sebastian; Schneider, Carsten Determining the closed forms of the anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. (English) Zbl 1197.81037 Comput. Phys. Commun. 180, No. 11, 2143-2165 (2009). MSC: 81T80 33F05 68W30 PDFBibTeX XMLCite \textit{J. Blümlein} et al., Comput. Phys. Commun. 180, No. 11, 2143--2165 (2009; Zbl 1197.81037) Full Text: DOI arXiv
Kauers, Manuel; Koutschan, Christoph A Mathematica package for \(q\)-holonomic sequences and power series. (English) Zbl 1180.33030 Ramanujan J. 19, No. 2, 137-150 (2009). MSC: 33F10 05A30 11B65 39A10 68N30 PDFBibTeX XMLCite \textit{M. Kauers} and \textit{C. Koutschan}, Ramanujan J. 19, No. 2, 137--150 (2009; Zbl 1180.33030) Full Text: DOI
Kauers, Manuel; Zimmermann, Burkhard Computing the algebraic relations of \(C\)-finite sequences and multisequences. (English) Zbl 1163.11084 J. Symb. Comput. 43, No. 11, 787-803 (2008). Reviewer: Zhi-Wei Sun (Nanjing) MSC: 11Y16 11B37 PDFBibTeX XMLCite \textit{M. Kauers} and \textit{B. Zimmermann}, J. Symb. Comput. 43, No. 11, 787--803 (2008; Zbl 1163.11084) Full Text: DOI
Kauers, Manuel Solving difference equations whose coefficients are not transcendental. (English) Zbl 1158.39003 Theor. Comput. Sci. 401, No. 1-3, 217-227 (2008). Reviewer: Edwin Engin Yaz (Milwaukee) MSC: 39A10 40A05 65Q05 40C05 PDFBibTeX XMLCite \textit{M. Kauers}, Theor. Comput. Sci. 401, No. 1--3, 217--227 (2008; Zbl 1158.39003) Full Text: DOI
Kauers, Manuel Summation algorithms for Stirling number identities. (English) Zbl 1142.11008 J. Symb. Comput. 42, No. 10, 948-970 (2007). Reviewer: Ping Sun (Shenyang) MSC: 11B73 05A19 PDFBibTeX XMLCite \textit{M. Kauers}, J. Symb. Comput. 42, No. 10, 948--970 (2007; Zbl 1142.11008) Full Text: DOI