Fetching the paper…
Reading the bibliography…
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$.
Fasenmyer, M. C., November 1945. Some generalized hypergeometric polynomials. Ph.D. thesis, University of Michigan
1945
Earlier work this paper cites.
Feynman, R., 1949. Space-time approach to quantum electrodynamics. Phys. Rev. D76, 769–789
1949
Earlier work this paper cites.
Wick, G., 1950. The evaluation of the collision matrix. Phys. Rev. 80, 268–272
1950
Earlier work this paper cites.
Naas, J., Schmid, H. (Eds.), 1961. Mathematisches Wörterbuch. Vol. II. Teubnerberlag Leipzig and Akademie Verlag, Berlin
1961
Earlier work this paper cites.
Gosper, Jr., R. W., 1978. Decision procedure for indefinite hypergeometric summation. Proc. Nat. Acad. Sci. U.S.A. 75 (1), 40–42
1978
Earlier work this paper cites.
Karr, M., 1981. Summation in finite terms. J. ACM 28 (2), 305–350
1981
Earlier work this paper cites.
Petkovšek, M., 1992. Hypergeometric solutions of linear recurrences with polynomial coefficients. J. Symb. Comp. 14, 243–264
1992
Earlier work this paper cites.
Wilf, H. S., Zeilberger, D., 1992. An algorithmic proof theory for hypergeometric (ordinary and “ q q ”) multisum/integral identities. Invent. Math. 108 (3), 575–633
1992
Earlier work this paper cites.
Abramov, S., Petkovšek, M., 1994. D’Alembertian solutions of linear differential and difference equations. In: von zur Gathen, J. (Ed.), Proc. ISSAC’94. ACM Press, pp. 169–174
1994
Earlier work this paper cites.
Paule, P., 1995. Greatest factorial factorization and symbolic summation. J. Symbolic Comput. 20 (3), 235–268
1995
Earlier work this paper cites.
Paule, P., Schorn, M., 1995. A Mathematica Version of Zeilberger’s Algorithm for Proving Binomial Coefficient Identities. J. Symbolic Comput. 20, 673–698
1995
Earlier work this paper cites.
Petkovšek, M., Wilf, H. S., Zeilberger, D., 1996. A = B A=B . A. K. Peters, Wellesley, MA
1996
Earlier work this paper cites.
Whittaker, E., Watson, G., 1996. A Course of Modern Analysis. Cambridge Mathematical Library Series. Cambridge University Press, Cambridge
1996
Earlier work this paper cites.
Chyzak, F., 2000. An extension of Zeilberger’s fast algorithm to general holonomic functions. Discrete Math. 217 (1-3), 115–134, fPSAC 1997
1997
Earlier work this paper cites.
Wegschaider, K., May 1997. Computer generated proofs of binomial multi-sum identities. Master’s thesis, RISC, Johannes Kepler University
1997
Cited alongside, same era.
Andrews, G. E., Askey, R., Roy, R., 1999. Special functions. Vol. 71 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge
1999
Cited alongside, same era.
Blümlein, J., Kurth, S., 1999. Harmonic sums and Mellin transforms up to two-loop order. Phys. Rev. D60, 014018, [arXiv:hep-ph/9810241]
1999
Cited alongside, same era.
Broadhurst, D. J., 1999. Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity. Eur. Phys. J. 8, 311–333, [arXiv:hep-th/9803091]
1999
Cited alongside, same era.
Blümlein, J., 2000. Analytic continuation of mellin transforms up to two-loop order. Comput. Phys. Commun. 133, 76–104, [arXiv:hep-ph/0003100]
2008
Later among the works it cites.
Schneider, C., 2008. A refined difference field theory for symbolic summation. J. Symbolic Comput. 43 (9), 611–644
2008
Later among the works it cites.
Ablinger, J., February 2009. A computer algebra toolbox for harmonic sums related to particle physics. Master’s thesis, RISC, Johannes Kepler University
2009
Later among the works it cites.
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2000
Cited alongside, same era.
Paris, R., Kaminski, D., 2001. Asymptotics and Mellin-Barnes Integrals. Vol. 85 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge
2001
Cited alongside, same era.
Schneider, C., May 2001. Symbolic Summation in Difference Fields. Ph.D. thesis, RISC, J. Kepler University Linz
2001
Cited alongside, same era.
Moch, S., Uwer, P., Weinzierl, S., 2002. Nested sums, expansion of transcendental functions, and multiscale multiloop integrals. J. Math. Phys. 43, 3363–3386
2002
Cited alongside, same era.
Blümlein, J., 2004. Algebraic relations between harmonic sums and associated quantities. Comput. Phys. Commun. 159 (1), 19–54, [arXiv:hep-ph/0311046]
2004
Cited alongside, same era.
Blümlein, J., Moch, S. O., 2005. Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions 614, 53–61, [arXiv:hep-ph/0503188]
2005
Cited alongside, same era.
Apagodu, M., Zeilberger, D., 2006. Multi-variable Zeilberger and Almkvist–Zeilberger algorithms and the sharpening of Wilf–Zeilberger theory. Advances in Applied Math. 37, 139–152
2006
Cited alongside, same era.
Blümlein, J., Freitas, A. D., van Neerven, W. L., Klein, S., 2006. The longitudinal heavy quark structure function F L Q Q ¯ F_{L}^{Q\overline{Q}} in the region Q 2 ≫ m 2 Q^{2}\gg m^{2} at O ( α s 3 ) O(\alpha_{s}^{3})
2006
Cited alongside, same era.
2009
Later among the works it cites.
Koutschan, C., September 2009. Advanced applications of the holonomic systems approach. Ph.D. thesis, RISC, Johannes Kepler University
2009
Later among the works it cites.
Blümlein, J., 2010. Structural relations of harmonic sums and Mellin transforms at weight w = 6 w=6 . In: Motives, quantum field theory, and pseudodifferential operators. Vol. 12 of Clay Math. Proc. Amer. Math. Soc., pp. 167–187
2010
Closest in time.
2010
Closest in time.
2010
Closest in time.
Schneider, C., 2010. A symbolic summation approach to find optimal nested sum representations. In: Motives, quantum field theory, and pseudodifferential operators. Vol. 12 of Clay Math. Proc. Amer. Math. Soc., pp. 285–308
2010
Closest in time.
Stan, F., 2010. Algorithms for special functions: Computer algebra and analytical aspects. Ph.D. thesis, RISC, Johannes Kepler University Linz
2010
Closest in time.
Abramov, S., Bronstein, M., Petkovšek, M., Schneider, C., 2011. In preparation
2011
Closest in time.
Kauers, M., Schneider, C., 2006. Indefinite summation with unspecified summands. Discrete Math. 306 (17), 2021–2140
2021
Closest in time.
Vermaseren, J., 1999. Harmonic sums, Mellin transforms and integrals. Int. J. Mod. Phys. A14, 2037–2976
2037
Closest in time.