{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T03:14:33Z","timestamp":1775099673940,"version":"3.50.1"},"publisher-location":"Cham","reference-count":66,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319150802","type":"print"},{"value":"9783319150819","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-15081-9_10","type":"book-chapter","created":{"date-parts":[[2015,1,20]],"date-time":"2015-01-20T05:35:27Z","timestamp":1421732127000},"page":"157-191","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Fast Algorithms for Refined Parameterized Telescoping in Difference Fields"],"prefix":"10.1007","author":[{"given":"Carsten","family":"Schneider","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,1,21]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.nuclphysb.2012.06.007","volume":"864","author":"J Ablinger","year":"2012","unstructured":"Ablinger, J., Bl\u00fcmlein, J., Hasselhuhn, A., Klein, S., Schneider, C., Wissbrock, F.: Massive 3-loop ladder diagrams for quarkonic local operator matrix elements. Nucl. Phys. B. 864, 52\u201384 (2012). ArXiv:1206.2252v1 [hep-ph]","journal-title":"Nucl. Phys. B."},{"key":"10_CR2","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.nuclphysb.2010.10.021","volume":"844","author":"J Ablinger","year":"2011","unstructured":"Ablinger, J., Bl\u00fcmlein, J., Klein, S., Schneider, C., Wissbrock, F.: 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, 26\u201354 (2011). ArXiv:1008.3347 [hep-ph]","journal-title":"Nucl. Phys. B."},{"issue":"10","key":"10_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.3629472","volume":"52","author":"J Ablinger","year":"2011","unstructured":"Ablinger, J., Bl\u00fcmlein, J., Schneider, C.: Harmonic sums and polylogarithms generated by cyclotomic polynomials. J. Math. Phys. 52(10), 1\u201352 (2011). arXiv:1007.0375 [hep-ph]","journal-title":"J. Math. Phys."},{"issue":"8","key":"10_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.4811117","volume":"54","author":"J Ablinger","year":"2013","unstructured":"Ablinger, J., Bl\u00fcmlein, J., Schneider, C.: Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms. J. Math. Phys. 54(8), 1\u201374 (2013). ArXiv:1302.0378 [math-ph]","journal-title":"J. Math. Phys."},{"key":"10_CR5","first-page":"1071","volume":"11","author":"SA Abramov","year":"1971","unstructured":"Abramov, S.A.: On the summation of rational functions. Zh. vychisl. mat. Fiz. 11, 1071\u20131074 (1971)","journal-title":"Zh. vychisl. mat. Fiz."},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/0041-5553(75)90181-0","volume":"15","author":"SA Abramov","year":"1975","unstructured":"Abramov, S.A.: The rational component of the solution of a first-order linear recurrence relation with a rational right-hand side. U.S.S.R. Comput. Math. Math. Phys. 15, 216\u2013221 (1975). Transl. from Zh. vychisl. mat. mat. fiz. 15, 1035\u20131039 (1975)","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"issue":"6","key":"10_CR7","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/S0041-5553(89)80002-3","volume":"29","author":"SA Abramov","year":"1989","unstructured":"Abramov, S.A.: Rational solutions of linear differential and difference equations with polynomial coefficients. U.S.S.R. Comput. Math. Math. Phys. 29(6), 7\u201312 (1989)","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"key":"10_CR8","unstructured":"Abramov, S.A., Bronstein, M., Petkov\u0161ek, M., Schneider, C.: (2015, In preparation)"},{"key":"10_CR9","doi-asserted-by":"crossref","unstructured":"Abramov, S.A., Petkov\u0161ek, M.: D\u2019Alembertian solutions of linear differential and difference equations. In: von zur Gathen, J. (ed.) Proceedings of ISSAC 1994, pp. 169\u2013174. ACM Press (1994)","DOI":"10.1145\/190347.190412"},{"issue":"5","key":"10_CR10","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1006\/jsco.2002.0522","volume":"33","author":"SA Abramov","year":"2002","unstructured":"Abramov, S.A., Petkov\u0161ek, M.: Rational normal forms and minimal decompositions of hypergeometric terms. J. Symbolic Comput. 33(5), 521\u2013543 (2002)","journal-title":"J. Symbolic Comput."},{"issue":"6","key":"10_CR11","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1016\/j.jsc.2010.03.001","volume":"45","author":"SA Abramov","year":"2010","unstructured":"Abramov, S.A., Petkov\u0161ek, M.: Polynomial ring automorphisms, rational $$(w,\\sigma )$$-canonical forms, and the assignment problem. J. Symbolic Comput. 45(6), 684\u2013708 (2010)","journal-title":"J. Symbolic Comput."},{"issue":"4","key":"10_CR12","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1016\/j.aam.2004.07.008","volume":"34","author":"GE Andrews","year":"2005","unstructured":"Andrews, G.E., Paule, P., Schneider, C.: Plane partitions VI: stembridge\u2019s TSPP theorem. Adv. Appl. Math. 34(4), 709\u2013739 (2005). Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud","journal-title":"Adv. Appl. Math."},{"issue":"4\u20135","key":"10_CR13","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1006\/jsco.1999.0321","volume":"28","author":"A Bauer","year":"1999","unstructured":"Bauer, A., Petkov\u0161ek, M.: Multibasic and mixed hypergeometric Gosper-type algorithms. J. Symbolic Comput. 28(4\u20135), 711\u2013736 (1999)","journal-title":"J. Symbolic Comput."},{"issue":"1\u20132","key":"10_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.nuclphysb.2008.05.016","volume":"803","author":"I Bierenbaum","year":"2008","unstructured":"Bierenbaum, I., Bl\u00fcmlein, J., Klein, S., Schneider, C.: Two-loop massive operator matrix elements for unpolarized heavy flavor production to $$O(\\epsilon )$$. Nucl. Phys. B. 803(1\u20132), 1\u201341 (2008). arXiv:hep-ph\/0803.0273","journal-title":"Nucl. Phys. B."},{"key":"10_CR15","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.nuclphysb.2012.09.001","volume":"866","author":"J Bl\u00fcmlein","year":"2013","unstructured":"Bl\u00fcmlein, J., Hasselhuhn, A., Klein, S., Schneider, C.: The $$O(\\alpha _s^3 n_f T_F^2 C_{A, F})$$ contributions to the gluonic massive operator matrix elements. Nucl. Phys. B. 866, 196\u2013211 (2013)","journal-title":"Nucl. Phys. B."},{"key":"10_CR16","doi-asserted-by":"publisher","first-page":"1267","DOI":"10.1016\/j.jsc.2011.12.044","volume":"47","author":"J Bl\u00fcmlein","year":"2012","unstructured":"Bl\u00fcmlein, J., Klein, S., Schneider, C., Stan, F.: A symbolic summation approach to feynman integral calculus. J. Symbolic Comput. 47, 1267\u20131289 (2012)","journal-title":"J. Symbolic Comput."},{"key":"10_CR17","first-page":"014018","volume":"D60","author":"J Bl\u00fcmlein","year":"1999","unstructured":"Bl\u00fcmlein, J., Kurth, S.: Harmonic sums and Mellin transforms up to two-loop order. Phys. Rev. D60, 014018 (1999)","journal-title":"Phys. Rev."},{"issue":"6","key":"10_CR18","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1006\/jsco.2000.0368","volume":"29","author":"M Bronstein","year":"2000","unstructured":"Bronstein, M.: On solutions of linear ordinary difference equations in their coefficient field. J. Symbolic Comput. 29(6), 841\u2013877 (2000)","journal-title":"J. Symbolic Comput."},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"Chen, S., Jaroschek, M., Kauers, M., Singer, M.F.: Desingularization explains order-degree curves for ore operators. In: Kauers, M. (ed.) Proceedings of ISSAC 2013, pp. 157\u2013164 (2013)","DOI":"10.1145\/2465506.2465510"},{"key":"10_CR20","doi-asserted-by":"crossref","unstructured":"Chen, S., Kauers, M.: Order-degree curves for hypergeometric creative telescoping. In: van der Hoeven, J., van Hoeij, M. (eds.) Proceedings of ISSAC 2012, pp. 122\u2013129 (2012)","DOI":"10.1145\/2442829.2442850"},{"key":"10_CR21","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/S0012-365X(99)00259-9","volume":"217","author":"F Chyzak","year":"2000","unstructured":"Chyzak, F.: An extension of Zeilberger\u2019s fast algorithm to general holonomic functions. Discrete Math. 217, 115\u2013134 (2000)","journal-title":"Discrete Math."},{"key":"10_CR22","volume-title":"Difference Algebra","author":"RM Cohn","year":"1965","unstructured":"Cohn, R.M.: Difference Algebra. Interscience Publishers, John Wiley & Sons, New York (1965)"},{"issue":"3","key":"10_CR23","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s11139-006-0144-5","volume":"12","author":"K Driver","year":"2006","unstructured":"Driver, K., Prodinger, H., Schneider, C., Weideman, J.A.C.: Pad\u00e9 approximations to the logarithm III: alternative methods and additional results. Ramanujan J. 12(3), 299\u2013314 (2006)","journal-title":"Ramanujan J."},{"key":"10_CR24","unstructured":"Er\u00f6cal, B.: Algebraic extensions for summation in finite terms. Ph.D. thesis, RISC, Johannes Kepler University, Linz (2011)"},{"key":"10_CR25","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1073\/pnas.75.1.40","volume":"75","author":"RW Gosper","year":"1978","unstructured":"Gosper, R.W.: Decision procedures for indefinite hypergeometric summation. Proc. Nat. Acad. Sci. U.S.A. 75, 40\u201342 (1978)","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"issue":"3","key":"10_CR26","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1006\/jsco.1998.0251","volume":"27","author":"PA Hendriks","year":"1999","unstructured":"Hendriks, P.A., Singer, M.F.: Solving difference equations in finite terms. J. Symbolic Comput. 27(3), 239\u2013259 (1999)","journal-title":"J. Symbolic Comput."},{"key":"10_CR27","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1145\/322248.322255","volume":"28","author":"M Karr","year":"1981","unstructured":"Karr, M.: Summation in finite terms. J. ACM 28, 305\u2013350 (1981)","journal-title":"J. ACM"},{"key":"10_CR28","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/S0747-7171(85)80038-9","volume":"1","author":"M Karr","year":"1985","unstructured":"Karr, M.: Theory of summation in finite terms. J. Symbolic Comput. 1, 303\u2013315 (1985)","journal-title":"J. Symbolic Comput."},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Kauers, M., Schneider, C.: Application of unspecified sequences in symbolic summation. In: Dumas, J. (ed.) Proceedings of ISSAC 2006, pp. 177\u2013183. ACM Press (2006)","DOI":"10.1145\/1145768.1145800"},{"issue":"17","key":"10_CR30","doi-asserted-by":"publisher","first-page":"2021","DOI":"10.1016\/j.disc.2006.04.005","volume":"306","author":"M Kauers","year":"2006","unstructured":"Kauers, M., Schneider, C.: Indefinite summation with unspecified summands. Discrete Math. 306(17), 2021\u20132140 (2006)","journal-title":"Discrete Math."},{"key":"10_CR31","doi-asserted-by":"crossref","unstructured":"Kauers, M., Schneider, C.: Symbolic summation with radical expressions. In: Brown, C. (ed.) Proceedings of ISSAC 2007, pp. 219\u2013226 (2007)","DOI":"10.1145\/1277548.1277579"},{"key":"10_CR32","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0377-0427(93)90317-5","volume":"48","author":"TH Koornwinder","year":"1993","unstructured":"Koornwinder, T.H.: On Zeilberger\u2019s algorithm and its $$q$$-analogue. J. Comp. Appl. Math. 48, 91\u2013111 (1993)","journal-title":"J. Comp. Appl. Math."},{"key":"10_CR33","doi-asserted-by":"crossref","unstructured":"Koutschan, C.: Creative telescoping for holonomic functions. In: Schneider, C., Bl\u00fcmlein, J. (eds.) Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions. Texts and Monographs in Symbolic Computation, pp. 171\u2013194. Springer (2013). ArXiv:1307.4554 [cs.SC]","DOI":"10.1007\/978-3-7091-1616-6_7"},{"key":"10_CR34","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1515\/crll.1835.13.93","volume":"13","author":"J Liouville","year":"1835","unstructured":"Liouville, J.: M\u00e9moire sur l\u2019int\u00e9gration d\u2019une classe de fonctions transcendantes. J. Reine Angew. Math. 13, 93\u2013118 (1835)","journal-title":"J. Reine Angew. Math."},{"key":"10_CR35","doi-asserted-by":"publisher","first-page":"3363","DOI":"10.1063\/1.1471366","volume":"6","author":"SO Moch","year":"2002","unstructured":"Moch, S.O., Uwer, P., Weinzierl, S.: Nested sums, expansion of transcendental functions, and multiscale multiloop integrals. J. Math. Phys. 6, 3363\u20133386 (2002)","journal-title":"J. Math. Phys."},{"issue":"265","key":"10_CR36","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1090\/S0025-5718-08-02118-2","volume":"78","author":"R Osburn","year":"2009","unstructured":"Osburn, R., Schneider, C.: Gaussian hypergeometric series and extensions of supercongruences. Math. Comp. 78(265), 275\u2013292 (2009)","journal-title":"Math. Comp."},{"issue":"3","key":"10_CR37","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1995.1049","volume":"20","author":"P Paule","year":"1995","unstructured":"Paule, P.: Greatest factorial factorization and symbolic summation. J. Symbolic Comput. 20(3), 235\u2013268 (1995)","journal-title":"J. Symbolic Comput."},{"key":"10_CR38","unstructured":"Paule, P.: Contiguous relations and creative telescoping, p. 33. Unpublished manuscript (2001)"},{"key":"10_CR39","doi-asserted-by":"crossref","unstructured":"Paule, P., Riese, A.: A Mathematica q-analogue of Zeilberger\u2019s algorithm based on an algebraically motivated aproach to $$q$$-hypergeometric telescoping. In: Ismail, M., Rahman, M. (eds.) Special Functions, q-Series and Related Topics, vol. 14, pp. 179\u2013210. AMS (1997)","DOI":"10.1090\/fic\/014\/11"},{"issue":"2","key":"10_CR40","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/S0196-8858(03)00016-2","volume":"31","author":"P Paule","year":"2003","unstructured":"Paule, P., Schneider, C.: Computer proofs of a new family of harmonic number identities. Adv. Appl. Math. 31(2), 359\u2013378 (2003)","journal-title":"Adv. Appl. Math."},{"issue":"5\u20136","key":"10_CR41","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1006\/jsco.1995.1071","volume":"20","author":"P Paule","year":"1995","unstructured":"Paule, P., Schorn, M.: A Mathematica version of Zeilberger\u2019s algorithm for proving binomial coefficient identities. J. Symbolic Comput. 20(5\u20136), 673\u2013698 (1995)","journal-title":"J. Symbolic Comput."},{"key":"10_CR42","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/978-3-642-54479-8_6","volume-title":"Algebraic and Algorithmic Aspects of Differential and Integral Operators","author":"C Koutschan","year":"2014","unstructured":"Koutschan, C., Paule, P., Suslov, S.K.: Relativistic coulomb integrals and Zeilberger\u2019s holonomic systems approach II. In: Barkatou, M., Cluzeau, T., Regensburger, G., Rosenkranz, M. (eds.) AADIOS 2012. LNCS, vol. 8372, pp. 135\u2013145. Springer, Heidelberg (2014)"},{"issue":"2\u20133","key":"10_CR43","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0747-7171(92)90038-6","volume":"14","author":"M Petkov\u0161ek","year":"1992","unstructured":"Petkov\u0161ek, M.: Hypergeometric solutions of linear recurrences with polynomial coefficients. J. Symbolic Comput. 14(2\u20133), 243\u2013264 (1992)","journal-title":"J. Symbolic Comput."},{"key":"10_CR44","volume-title":"$$A=B$$","author":"M Petkov\u0161ek","year":"1996","unstructured":"Petkov\u0161ek, M., Wilf, H.S., Zeilberger, D.: $$A=B$$. A. K. Peters, Wellesley (1996)"},{"key":"10_CR45","doi-asserted-by":"crossref","unstructured":"Petkov\u0161ek, M., Zakraj\u0161ek, H.: Solving linear recurrence equations with polynomial coefficients. In: Schneider, C., Bl\u00fcmlein, J. (eds.) Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions. Texts and Monographs in Symbolic Computation, pp. 259\u2013284. Springer (2013)","DOI":"10.1007\/978-3-7091-1616-6_11"},{"issue":"5\u20136","key":"10_CR46","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1006\/jsco.1995.1068","volume":"20","author":"R Pirastu","year":"1995","unstructured":"Pirastu, R., Strehl, V.: Rational summation and Gosper-Petkov\u0161ek representation. J. Symbolic Comput. 20(5\u20136), 617\u2013635 (1995)","journal-title":"J. Symbolic Comput."},{"key":"10_CR47","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.1016\/j.ejc.2011.04.002","volume":"32","author":"H Prodinger","year":"2011","unstructured":"Prodinger, H., Schneider, C., Wagner, S.: Unfair permutations. Europ. J. Comb. 32, 1282\u20131298 (2011)","journal-title":"Europ. J. Comb."},{"key":"10_CR48","unstructured":"Schneider, C.: Symbolic summation in difference fields. Technical report 01\u201317, RISC-Linz, J. Kepler University (2001). Ph.D. Thesis"},{"key":"10_CR49","unstructured":"Schneider, C.: Solving parameterized linear difference equations in $$\\mathit{\\Pi }{\\varSigma }$$-fields. SFB-Report 02\u201319, J. Kepler University, Linz (2002)"},{"key":"10_CR50","unstructured":"Schneider, C.: A collection of denominator bounds to solve parameterized linear difference equations in $$\\mathit{\\Pi }{\\varSigma }$$-extensions. An. Univ. Timi\u015foara Ser. Mat.-Inform. 42(2), 163\u2013179 (2004). Extended version of Proceedings of SYNASC 2004"},{"key":"10_CR51","doi-asserted-by":"crossref","unstructured":"Schneider, C.: Symbolic summation with single-nested sum extensions. In: Gutierrez, J. (ed.) Proceedings of ISSAC 2004, pp. 282\u2013289. ACM Press (2004)","DOI":"10.1145\/1005285.1005326"},{"issue":"1","key":"10_CR52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00200-004-0167-3","volume":"16","author":"C Schneider","year":"2005","unstructured":"Schneider, C.: Degree bounds to find polynomial solutions of parameterized linear difference equations in $$\\mathit{\\Pi }{\\varSigma }$$-fields. Appl. Algebra Engrg. Comm. Comput. 16(1), 1\u201332 (2005)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"10_CR53","doi-asserted-by":"crossref","unstructured":"Schneider, C.: Finding telescopers with minimal depth for indefinite nested sum and product expressions. In: Kauers, M. (ed.) Proceedings of ISSAC 2005, pp. 285\u2013292. ACM (2005)","DOI":"10.1145\/1073884.1073924"},{"issue":"4","key":"10_CR54","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1016\/j.aam.2004.07.009","volume":"34","author":"C Schneider","year":"2005","unstructured":"Schneider, C.: A new Sigma approach to multi-summation. Adv. Appl. Math. 34(4), 740\u2013767 (2005)","journal-title":"Adv. Appl. Math."},{"issue":"1","key":"10_CR55","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s00026-005-0242-2","volume":"9","author":"C Schneider","year":"2005","unstructured":"Schneider, C.: Product representations in $$\\mathit{\\Pi }{\\varSigma }$$-fields. Ann. Comb. 9(1), 75\u201399 (2005)","journal-title":"Ann. Comb."},{"issue":"9","key":"10_CR56","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1080\/10236190500138262","volume":"11","author":"C Schneider","year":"2005","unstructured":"Schneider, C.: Solving parameterized linear difference equations in terms of indefinite nested sums and products. J. Differ. Eqn. Appl. 11(9), 799\u2013821 (2005)","journal-title":"J. Differ. Eqn. Appl."},{"issue":"3","key":"10_CR57","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1142\/S0219498807002302","volume":"6","author":"C Schneider","year":"2007","unstructured":"Schneider, C.: Simplifying sums in $$\\mathit{\\Pi }{\\varSigma }$$-Extensions. J. Algebra Appl. 6(3), 415\u2013441 (2007)","journal-title":"J. Algebra Appl."},{"key":"10_CR58","first-page":"1","volume":"56","author":"C Schneider","year":"2007","unstructured":"Schneider, C.: Symbolic summation assists combinatorics. S\u00e9m. Lothar. Combin. 56, 1\u201336 (2007). Article B56b","journal-title":"S\u00e9m. Lothar. Combin."},{"issue":"9","key":"10_CR59","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1016\/j.jsc.2008.01.001","volume":"43","author":"C Schneider","year":"2008","unstructured":"Schneider, C.: A refined difference field theory for symbolic summation. J. Symbolic Comput. 43(9), 611\u2013644 (2008). arXiv:0808.2543v1","journal-title":"J. Symbolic Comput."},{"key":"10_CR60","unstructured":"Schneider, C.: A symbolic summation approach to find optimal nested sum representations. In: Carey, A., Ellwood, D., Paycha, S., Rosenberg, S. (eds.) Motives, Quantum Field Theory, and Pseudodifferential Operators, Clay Mathematics Proceedings, vol. 12, pp. 285\u2013308. Amer. Math. Soc. (2010). ArXiv:0808.2543"},{"issue":"4","key":"10_CR61","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s00026-011-0076-7","volume":"14","author":"C Schneider","year":"2010","unstructured":"Schneider, C.: Parameterized telescoping proves algebraic independence of sums. Ann. Comb. 14(4), 533\u2013552 (2010). arXiv:0808.2596","journal-title":"Ann. Comb."},{"issue":"1","key":"10_CR62","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00200-009-0115-3","volume":"21","author":"C Schneider","year":"2010","unstructured":"Schneider, C.: Structural theorems for symbolic summation. Appl. Algebra Engrg. Comm. Comput. 21(1), 1\u201332 (2010)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"10_CR63","unstructured":"Schneider, C.: Modern summation methods for loop integrals in quantum field theory: The packages Sigma, EvaluateMultiSums and SumProduction. In: Proceedings of ACAT 2013, To appear in J. Phys.: Conf. Ser., pp. 1\u201317 (2014). ArXiv:1310.0160 [cs.SC]"},{"key":"10_CR64","doi-asserted-by":"crossref","unstructured":"Schneider, C.: Simplifying multiple sums in difference fields. In: Schneider, C., Bl\u00fcmlein, J. (eds.) Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions. Texts and Monographs in Symbolic Computation, pp. 325\u2013360. Springer (2013). ArXiv:1304.4134 [cs.SC]","DOI":"10.1007\/978-3-7091-1616-6_14"},{"key":"10_CR65","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1142\/S0217751X99001032","volume":"A14","author":"JAM Vermaseren","year":"1999","unstructured":"Vermaseren, J.A.M.: Harmonic sums, Mellin transforms and integrals. Int. J. Mod. Phys. A14, 2037\u20132976 (1999)","journal-title":"Int. J. Mod. Phys."},{"key":"10_CR66","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0747-7171(08)80044-2","volume":"11","author":"D Zeilberger","year":"1991","unstructured":"Zeilberger, D.: The method of creative telescoping. J. Symbolic Comput. 11, 195\u2013204 (1991)","journal-title":"J. Symbolic Comput."}],"container-title":["Lecture Notes in Computer Science","Computer Algebra and Polynomials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-15081-9_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T12:37:54Z","timestamp":1676637474000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-15081-9_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319150802","9783319150819"],"references-count":66,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-15081-9_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"21 January 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}