Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case

Nuclear Physics B

Volumn 836, Issue 3, 2010, Pages 129-170

  Bytev, Vladimir V ^a   Kalmykov, Mikhail Yu ^a   Kniehl, Bernd A ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Differential reduction; Generalized hypergeometric functions; Laurent expansion; Multiloop calculations

Indexed keywords

EID: 77952883524     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2010.03.025     Document Type: Article

References (103)

1. 't Hooft G., Veltman M. Nucl. Phys. B 1972, 44:189.
2. Anastasiou C., Melnikov K. Nucl. Phys. B 2002, 646:220.
3. Regge T. Battelle Rencontres: 1967 Lectures in Mathematics and Physics 1968, 433-458. W.A. Benjamin, New York. C.M. DeWitt, J.A. Wheeler (Eds.).
4. de Calan C., Malbouisson A.P.C. Ann. Poincaré Phys. Theor. 1980, 32:91.
5. de Calan C., David F., Rivasseau V. Commun. Math. Phys. 1981, 78:531.
6. de Calan C., Malbouisson A.P.C. Commun. Math. Phys. 1983, 90:413.
7. Smirnov V.A. Feynman Integral Calculus 2006, Springer, Berlin.
8. Del Duca V., Duhr C., Glover E.W.N., Smirnov V.A. JHEP 2010, 1001:042.
9. Kershaw D.S. Phys. Rev. D 1973, 8:2708.
10. Wu A.C.T. Phys. Rev. D 1974, 9:370.
11. Mano K. Phys. Rev. D 1975, 11:452.
12. Gel'fand I.M., Graev M.I., Retakh V.S. Russian Math. Sur. 1992, 47:1.
13. Higher Transcendental Functions 1953, McGraw-Hill, New York. A. Erdelyi (Ed.).
14. Ore O. J. Math. Pure Appl. 1930, 9:311.
15. Sato M. Nagoya Math. J. 1990, 120:1.
16. Kalmykov M.Yu., Bytev V.V., Kniehl B.A., Ward B.F.L., Yost S.A. PoS(ACAT08) 2008, 125. arxiv:/0901.4716.
17. Takayama N. Jpn. J. Appl. Math. 1989, 6:147.
18. Gauss C.F. Gesammelte Werke 1823, vol. 3:1866-1929. Teubner, Leipzig.
19. Tarasov O.V. Acta Phys. Pol. B 1998, 29:2655.
20. Tarasov O.V. Nucl. Instrum. Methods A 2004, 534:293.
21. Tkachov F.V. Phys. Lett. B 1981, 100:65.
22. Chetyrkin K.G., Tkachov F.V. Nucl. Phys. B 1981, 192:159.
23. Kalmykov M.Yu., Ward B.F.L., Yost S. JHEP 2007, 0702:040.
24. Kalmykov M.Yu., Ward B.F.L., Yost S. JHEP 2007, 0710:048.
25. Yost S.A., Kalmykov M.Yu., Ward B.F.L. in: Proceedings of the 34th International Conference in High Energy Physics (ICHEP08), Philadelphia, USA, 2008, eConf C080730. arxiv:/0808.2605.
26. Kalmykov M.Yu., Ward B.F.L., Yost S. JHEP 2007, 0711:009.
27. Kalmykov M.Yu., Kniehl B.A. Nucl. Phys. B 2009, 809:365.
28. Davydychev A.I., Kalmykov M.Yu. Nucl. Phys. B 2004, 699:3.
29. Rainville E.D. Bull. Amer. Math. Soc. 1945, 51:714.
30. Takayama N. J. Symbolic Comput. 1995, 20:637.
31. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series. More Special Functions 1990, vol. 3. Gordon and Breach, New York.
32. Gottschalk J.E., Maslen E.N. J. Phys. A 1988, 21:1983.
33. Karlsson P.W. J. Math. Phys. 1971, 12:270.
34. Baikov P.A. Phys. Lett. B 2000, 474:385.
35. Baikov P.A. Phys. Lett. B 2006, 634:325.
36. Moch S., Uwer P., Weinzierl S. J. Math. Phys. 2002, 43:3363.
37. Weinzierl S. J. Math. Phys. 2004, 45:2656.
38. Davydychev A.I. Phys. Rev. D 2000, 61:087701.
39. Davydychev A.I., Kalmykov M.Yu. Nucl. Phys. B (Proc. Suppl.) 2000, 89:283.
40. Davydychev A.I., Kalmykov M.Yu. Nucl. Phys. B 2001, 605:266.
41. Kalmykov M.Yu., Kniehl B.A., Ward B.F.L., Yost S.A. in: V.A. Duk, V.A. Matveev, A.A. Rubakov (Eds.), Proceedings of the 15th International Seminar on High Energy Physics (QUARKS-2008), Sergiev Posad, Russia, 2008. arxiv:/0810.3238.
42. Kalmykov M.Yu. Nucl. Phys. B (Proc. Suppl.) 2004, 135:280.
43. Huber T., Maître D. Comput. Phys. Commun. 2008, 178:755.
44. Norlund N.E. Acta Math. 1955, 94:289.
45. Lappo-Danilevsky I.A. Mémoires sur la théorie des systémes des équations différentielles linéaires 1953, Chelsea, New York.
46. Goncharov A.B. Math. Res. Lett. 1997, 4:617.
47. Goncharov A.B. Math. Res. Lett. 1998, 5:497.
48. Remiddi E., Vermaseren J.A.M. Int. J. Mod. Phys. A 2000, 15:725.
49. Vollinga J., Weinzierl S. Comput. Phys. Commun. 2005, 167:177.
50. Kalmykov M.Yu. JHEP 2006, 0604:056.
51. Bytev V.V., Kalmykov M., Kniehl B.A., Ward B.F.L., Yost S.A. Proceedings of the International Linear Collider Workshop (LCWS08 and ILC08) 2009, Proceedings of Science, Trieste. arxiv:/0902.1352, T. Speer, F. Carminati, D. Peret-Gallix, R. Brun (Eds.).
52. Davydychev A.I. Phys. Lett. B 1991, 263:107.
53. Tarasov O.V. Phys. Rev. D 1996, 54:6479.
54. Boos E.E., Davydychev A.I. Theor. Math. Phys. 1991, 89:1052.
55. Berends F.A., Davydychev A.I., Smirnov V.A., Tausk J.B. Nucl. Phys. B 1995, 439:536.
56. Tarasov O.V. Nucl. Phys. B (Proc. Suppl.) 2000, 89:237.
57. Davydychev A.I. Nucl. Instrum. Methods A 2006, 559:293.
58. Anastasiou C., Glover E.W.N., Oleari C. Nucl. Phys. B 2000, 572:307.
59. Smirnov V.A. Commun. Math. Phys. 1990, 134:109.
60. Tkachov F.V. Int. J. Mod. Phys. A 1993, 8:2047.
61. Pivovarov G.B., Tkachov F.V. Int. J. Mod. Phys. A 1993, 8:2241.
62. Avdeev L.V. Comput. Phys. Commun. 1996, 98:15.
63. Jegerlehner F., Kalmykov M.Yu., Veretin O. Nucl. Phys. B 2002, 641:285.
64. Davydychev A.I. Loop calculations in QCD with massive quarks Presentation at International Conference on Relativistic Nuclear Dynamics, Vladivostok, Russia, 1991. http://wwwthep.physik.uni-mainz.de/~davyd/preprints/vladiv.pdf.
65. Broadhurst D.J., Fleischer J., Tarasov O.V. Z. Phys. C 1993, 60:287.
66. Tarasov O.V. Nucl. Phys. B 1997, 502:455.
67. Kalmykov M.Yu. http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html.
68. Jegerlehner F., Kalmykov M.Yu., Veretin O. Nucl. Phys. B 2003, 658:49.
69. Jegerlehner F., Kalmykov M.Yu., Veretin O. Nucl. Phys. B (Proc. Suppl.) 2003, 116:382.
70. Gluza J., Kajda K., Riemann T. Comput. Phys. Commun. 2007, 177:879.
71. Huber T. Nucl. Phys. B (Proc. Suppl.) 2008, 183:238.
72. Davydychev A.I., Tausk J.B. Nucl. Phys. B 1993, 397:123.
73. Broadhurst D.J. Eur. Phys. J. C 1999, 8:311.
74. Fleischer J., Kalmykov M.Yu. Phys. Lett. B 1999, 470:168.
75. Czakon M., Awramik M., Freitas A. Nucl. Phys. B (Proc. Suppl.) 2006, 157:58.
76. Tarasov O.V. Phys. Lett. B 2008, 670:67.
77. Kniehl B.A., Tarasov O.V. Nucl. Phys. B 2009, 820:178.
78. Bekavac S., Grozin A.G., Seidel D., Smirnov V.A. Nucl. Phys. B 2009, 819:183.
79. Davydychev A.I., Grozin A.G. Phys. Rev. D 1999, 59:054023.
80. Gray N., Broadhurst D.J., Grafe W., Schilcher K. Z. Phys. C 1990, 48:673.
81. Onishchenko A., Veretin O. Phys. Atom. Nucl. 2005, 68:1405.
82. Passarino G., Uccirati S. Nucl. Phys. B 2006, 747:113.
83. Actis S., Passarino G., Sturm C., Uccirati S. Nucl. Phys. B 2009, 811:182.
84. Frink A., Kniehl B.A., Kreimer D., Riesselmann K. Phys. Rev. D 1996, 54:4548.
85. Kniehl B.A., Kotikov A.V., Veretin O.L. Phys. Rev. Lett. 2008, 101:193401.
86. Kniehl B.A., Kotikov A.V., Veretin O.L. Phys. Rev. A 2009, 80:052501.
87. Vladimirov A.A. Theor. Math. Phys.. Teor. Mat. Fiz. 1980, 43:210.
88. Davydychev A.I. J. Math. Phys. 1991, 32:1052.
89. Broadhurst D.J., Gray N., Schilcher K. Z. Phys. C 1991, 52:111.
90. Davydychev A.I. J. Math. Phys. 1992, 33:358.
91. Broadhurst D.J. Z. Phys. C 1992, 54:599.
92. Berends F.A., Buza M., Böhm M., Scharf R. Z. Phys. C 1994, 63:227.
93. V.V. Bytev, M.Yu. Kalmykov, B.A. Kniehl, in preparation.
94. Bronstein M., Petkovšek M. Theoret. Comput. Sci. 1996, 157:3.
95. Chyzak F., Salvy B. J. Symbolic Comput. 1998, 26:187.
96. Chyzak F. Gröbner Bases, Symbolic Summation and Symbolic Integration. London Math. Soc. Lecture Notes Ser. 1998, vol. 251:32-60. Cambridge University Press, Cambridge.
97. Petkovšek M., Wilf H.S., Zeilberger D. A=B 1996, A.K. Peters, Natick, USA.
98. P. Paule, Contiguous relations and creative telescoping, Technical Report, RISC, Austria, 2001.
99. Laporta S. Int. J. Mod. Phys. A 2000, 15:5087.
100. Kalmykov M.Yu., Veretin O. Phys. Lett. B 2000, 483:315.
101. Borwein J.M., Broadhurst D.J., Kamnitzer J. Exper. Math. 2001, 10:25.
102. Kalmykov M.Y., Sheplyakov A. Comput. Phys. Commun. 2005, 172:45.
103. Lewin L. Polylogarithms and Associated Functions 1981, North-Holland, Amsterdam.