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Volumn 2007, Issue 10, 2007, Pages

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter

Author keywords

Integrable hierarchies; NLO computations

Indexed keywords


EID: 35748929393     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/10/048     Document Type: Article
Times cited : (42)

References (116)
  • 3
    • 0000396827 scopus 로고    scopus 로고
    • Analytical result for dimensionally regularized massless on-shell double box
    • V.A. Smirnov, Analytical result for dimensionally regularized massless on-shell double box 1999 Phys. Lett. B 460 397 [hep-ph/9905323]
    • (1999) Phys. Lett. , vol.460 , Issue.3-4 , pp. 397
    • Smirnov, V.A.1
  • 4
    • 0001718629 scopus 로고    scopus 로고
    • Non-planar massless two-loop Feynman diagrams with four on-shell legs
    • J.B. Tausk, Non-planar massless two-loop Feynman diagrams with four on-shell legs 1999 Phys. Lett. B 469 225 [hep-ph/9909506]
    • (1999) Phys. Lett. , vol.469 , Issue.1-4 , pp. 225
    • Tausk, J.B.1
  • 5
    • 0034736523 scopus 로고    scopus 로고
    • High-precision calculation of multi-loop Feynman integrals by difference equations
    • S. Laporta, High-precision calculation of multi-loop Feynman integrals by difference equations 2000 Int. J. Mod. Phys. A 15 5087 [hep-ph/0102033]
    • (2000) Int. J. Mod. Phys. , vol.15 , Issue.32 , pp. 5087
    • Laporta, S.1
  • 6
    • 33846135117 scopus 로고    scopus 로고
    • Numerical evaluation of loop integrals
    • C. Anastasiou and A. Daleo, Numerical evaluation of loop integrals 2006 J. High Energy Phys. JHEP10(2006)031 [hep-ph/0511176]
    • (2006) J. High Energy Phys. , vol.2006 , Issue.10 , pp. 031
    • Anastasiou, C.1    Daleo, A.2
  • 7
    • 33748798230 scopus 로고    scopus 로고
    • Automatized analytic continuation of Mellin-Barnes integrals
    • M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals 2006 Comput. Phys. Commun. 175 559 [hep-ph/0511200]
    • (2006) Comput. Phys. Commun. , vol.175 , Issue.8 , pp. 559
    • Czakon, M.1
  • 9
    • 33749008637 scopus 로고
    • A method of evaluating massive Feynman integrals
    • E.E. Boos and A.I. Davydychev, A method of evaluating massive Feynman integrals 1991 Theor. Math. Phys. 89 1052 [1991 Teor. Mat. Fiz. 89 56]
    • (1991) Theor. Math. Phys. , vol.89 , Issue.1 , pp. 1052
    • Boos, E.E.1    Davydychev, A.I.2
  • 10
    • 0003061686 scopus 로고
    • Two loop two point functions with masses: Asymptotic expansions and Taylor series, in any dimension
    • D.J. Broadhurst, J. Fleischer and O.V. Tarasov, Two loop two point functions with masses: asymptotic expansions and Taylor series, in any dimension 1993 Z. Physik C 60 287 [hep-ph/9304303]
    • (1993) Z. Physik , vol.60 , Issue.2 , pp. 287
    • Broadhurst, D.J.1    Fleischer, J.2    Tarasov, O.V.3
  • 11
    • 0033541916 scopus 로고    scopus 로고
    • Analytic two-loop results for self energy- and vertex-type diagrams with one non-zero mass
    • J. Fleischer, A.V. Kotikov and O.L. Veretin, Analytic two-loop results for self energy- and vertex-type diagrams with one non-zero mass 1999 Nucl. Phys. B 547 343 [hep-ph/9808242]
    • (1999) Nucl. Phys. , vol.547 , Issue.1-2 , pp. 343
    • Fleischer, J.1    Kotikov, A.V.2    Veretin, O.L.3
  • 12
    • 0034659038 scopus 로고    scopus 로고
    • Single-scale diagrams and multiple binomial sums
    • M.Y. Kalmykov and O. Veretin, Single-scale diagrams and multiple binomial sums 2000 Phys. Lett. B 483 315 [hep-th/0004010]
    • (2000) Phys. Lett. , vol.483 , Issue.1-3 , pp. 315
    • Kalmykov, M.Y.1    Veretin, O.2
  • 13
    • 0000376645 scopus 로고
    • Some exact results for N point massive Feynman integrals
    • A.I. Davydychev, Some exact results for N point massive Feynman integrals 1991 J. Math. Phys. 32 1052
    • (1991) J. Math. Phys. , vol.32 , Issue.4 , pp. 1052
    • Davydychev, A.I.1
  • 14
    • 34748819382 scopus 로고
    • General results for massive N point Feynman diagrams with different masses
    • A.I. Davydychev, General results for massive N point Feynman diagrams with different masses 1992 J. Math. Phys. 33 358
    • (1992) J. Math. Phys. , vol.33 , Issue.1 , pp. 358
    • Davydychev, A.I.1
  • 15
    • 0000776807 scopus 로고
    • Two loop selfenergy diagrams with different masses and the momentum expansion
    • A.I. Davydychev and J.B. Tausk, Two loop selfenergy diagrams with different masses and the momentum expansion 1993 Nucl. Phys. B 397 123
    • (1993) Nucl. Phys. , vol.397 , Issue.1-2 , pp. 123
    • Davydychev, A.I.1    Tausk, J.B.2
  • 16
    • 0001677138 scopus 로고    scopus 로고
    • A magic connection between massive and massless diagrams
    • A.I. Davydychev and J.B. Tausk, A magic connection between massive and massless diagrams 1996 Phys. Rev. D 53 7381 [hep-ph/9504431]
    • (1996) Phys. Rev. , vol.53 , Issue.12 , pp. 7381
    • Davydychev, A.I.1    Tausk, J.B.2
  • 17
    • 0002350876 scopus 로고
    • Closed expressions for specific massive multiloop selfenergy integrals
    • F.A. Berends, M. Buza, M. Böhm and R. Scharf, Closed expressions for specific massive multiloop selfenergy integrals 1994 Z. Physik C 63 227
    • (1994) Z. Physik , vol.63 , Issue.2 , pp. 227
    • Berends, F.A.1    Buza, M.2    Böhm, M.3    Scharf, R.4
  • 18
    • 0001722571 scopus 로고    scopus 로고
    • The Gegenbauer polynomial technique: The evaluation of a class of Feynman diagrams
    • A.V. Kotikov, The Gegenbauer polynomial technique: the evaluation of a class of Feynman diagrams 1996 Phys. Lett. B 375 240 [hep-ph/9512270]
    • (1996) Phys. Lett. , vol.375 , Issue.1-4 , pp. 240
    • Kotikov, A.V.1
  • 19
    • 0033074746 scopus 로고    scopus 로고
    • Two-loop QCD corrections of the massive fermion propagator
    • J. Fleischer, F. Jegerlehner, O.V. Tarasov and O.L. Veretin, Two-loop QCD corrections of the massive fermion propagator, 1999 Nucl. Phys. B 539 671 [Erratum 2000 Nucl. Phys. B 571 511] [hep-ph/9803493]
    • (1999) Nucl. Phys. , vol.539 , Issue.3 , pp. 671
    • Fleischer, J.1    Jegerlehner, F.2    Tarasov, O.V.3    Veretin, O.L.4
  • 20
    • 17144411516 scopus 로고    scopus 로고
    • Effect of M(C) on B quark chromomagnetic interaction and on-shell two-loop integrals with two masses
    • A.I. Davydychev and A.G. Grozin, Effect of M(C) on B quark chromomagnetic interaction and on-shell two-loop integrals with two masses 1999 Phys. Rev. D 59 054023 [hep-ph/9809589]
    • (1999) Phys. Rev. , vol.59 , Issue.5 , pp. 054023
    • Davydychev, A.I.1    Grozin, A.G.2
  • 21
    • 0000312513 scopus 로고    scopus 로고
    • The two-loop scalar and tensor pentabox graph with light-like legs
    • C. Anastasiou, E.W.N. Glover and C. Oleari, The two-loop scalar and tensor pentabox graph with light-like legs 2000 Nucl. Phys. B 575 416 [Erratum 2000 Nucl. Phys. B 585 763] [hep-ph/9912251]
    • (2000) Nucl. Phys. , vol.575 , Issue.1-2 , pp. 416
    • Anastasiou, C.1    Glover, E.W.N.2    Oleari, C.3
  • 22
    • 0037453738 scopus 로고    scopus 로고
    • General massive one-loop off-shell three-point functions
    • A.T. Suzuki, E.S. Santos and A.G.M. Schmidt, General massive one-loop off-shell three-point functions 2003 J. Phys. A: Math. Gen. 36 4465 [hep-ph/0210148]
    • (2003) J. Phys. A: Math. Gen. , vol.36 , Issue.15 , pp. 4465
    • Suzuki, A.T.1    Santos, E.S.2    Schmidt, A.G.M.3
  • 23
    • 0142231911 scopus 로고    scopus 로고
    • A new hypergeometric representation of one-loop scalar integrals in d dimensions
    • J. Fleischer, F. Jegerlehner and O.V. Tarasov, A new hypergeometric representation of one-loop scalar integrals in d dimensions 2003 Nucl. Phys. B 672 303 [hep-ph/0307113]
    • (2003) Nucl. Phys. , vol.672 , pp. 303
    • Fleischer, J.1    Jegerlehner, F.2    Tarasov, O.V.3
  • 24
    • 0344196689 scopus 로고    scopus 로고
    • The O(ααs) correction to the pole mass of the t-quark within the standard model
    • s) correction to the pole mass of the t-quark within the standard model 2004 Nucl. Phys. B 676 365 [hep-ph/0308216]
    • (2004) Nucl. Phys. , vol.676 , pp. 365
    • Jegerlehner, F.1    Kalmykov, M.Y.2
  • 25
    • 24044489948 scopus 로고    scopus 로고
    • Two-loop quark and gluon form factors in dimensional regularisation
    • T. Gehrmann, T. Huber and D. Matre, Two-loop quark and gluon form factors in dimensional regularisation 2005 Phys. Lett. B 622 295 [hep-ph/0507061]
    • (2005) Phys. Lett. , vol.622 , pp. 295
    • Gehrmann, T.1    Huber, T.2    Matre, D.3
  • 26
    • 33749346384 scopus 로고    scopus 로고
    • Hypergeometric representation of a four-loop vacuum bubble
    • E. Bejdakic and Y. Schröder, Hypergeometric representation of a four-loop vacuum bubble 2006 Nucl. Phys. (Proc. Suppl.) 160 155 [hep-ph/0607006]
    • (2006) Nucl. Phys. (Proc. Suppl.) , vol.160 , pp. 155
    • Bejdakic, E.1    Schröder, Y.2
  • 27
    • 33744973789 scopus 로고    scopus 로고
    • Hypergeometric representation of the two-loop equal mass sunrise diagram
    • O.V. Tarasov, Hypergeometric representation of the two-loop equal mass sunrise diagram 2006 Phys. Lett. B 638 195 [hep-ph/0603227]
    • (2006) Phys. Lett. , vol.638 , Issue.2-3 , pp. 195
    • Tarasov, O.V.1
  • 28
    • 34547665115 scopus 로고    scopus 로고
    • On one master integral for three-loop on-shell HQET propagator diagrams with mass
    • A.G. Grozin, T. Huber and D. Matre, On one master integral for three-loop on-shell HQET propagator diagrams with mass 2007 J. High Energy Phys. JHEP07(2007)033 [0705.2609]
    • (2007) J. High Energy Phys. , vol.2007 , Issue.7 , pp. 033
    • Grozin, A.G.1    Huber, T.2    Matre, D.3
  • 30
    • 0035797192 scopus 로고    scopus 로고
    • New results for the -expansion of certain one-, two- and three-loop Feynman diagrams
    • A.I. Davydychev and M.Y. Kalmykov, New results for the -expansion of certain one-, two- and three-loop Feynman diagrams 2001 Nucl. Phys. B 605 266 [hep-th/0012189]
    • (2001) Nucl. Phys. , vol.605 , Issue.1-3 , pp. 266
    • Davydychev, A.I.1    Kalmykov, M.Y.2
  • 31
    • 0037433828 scopus 로고    scopus 로고
    • Vs pole masses of gauge bosons. II: Two-loop electroweak fermion corrections
    • F. Jegerlehner, M.Y. Kalmykov and O. Veretin, vs pole masses of gauge bosons. II: two-loop electroweak fermion corrections, 2003 Nucl. Phys. B 658 49 [hep-ph/0212319]
    • (2003) Nucl. Phys. , vol.658 , pp. 49
    • Jegerlehner, F.1    Kalmykov, M.Y.2    Veretin, O.3
  • 32
    • 15344347616 scopus 로고    scopus 로고
    • Massive Feynman diagrams and inverse binomial sums
    • A.I. Davydychev and M.Y. Kalmykov, Massive Feynman diagrams and inverse binomial sums 2004 Nucl. Phys. B 699 3 [hep-th/0303162]
    • (2004) Nucl. Phys. , vol.699 , pp. 3
    • Davydychev, A.I.1    Kalmykov, M.Y.2
  • 33
    • 33646417318 scopus 로고    scopus 로고
    • Gauss hypergeometric function: Reduction, -expansion for integer/half-integer parameters and Feynman diagrams
    • M.Y. Kalmykov, Gauss hypergeometric function: reduction, -expansion for integer/half-integer parameters and Feynman diagrams 2006 J. High Energy Phys. JHEP04(2006)056 [hep-th/0602028]
    • (2006) J. High Energy Phys. , vol.2006 , Issue.4 , pp. 056
    • Kalmykov, M.Y.1
  • 34
    • 0010806732 scopus 로고
    • Three loop on-shell charge renormalization without integration: λ-MS (QED) to four loops
    • D.J. Broadhurst, Three loop on-shell charge renormalization without integration: λ-MS (QED) to four loops 1992 Z. Physik C 54 599
    • (1992) Z. Physik , vol.54 , Issue.4 , pp. 599
    • Broadhurst, D.J.1
  • 37
    • 0000855782 scopus 로고
    • Meditationes circa singulare serierum genus
    • L. Euler, Meditationes circa singulare serierum genus 1775 Novi Comm. Acad. Sci. Petropol. 20 140
    • (1775) Novi Comm. Acad. Sci. Petropol. , vol.20 , pp. 140
    • Euler, L.1
  • 39
    • 0000377345 scopus 로고    scopus 로고
    • Massive 3-loop feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity
    • D.J. Broadhurst, Massive 3-loop feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity 1999 Eur. Phys. J. C 8 311 [hep-th/9803091]
    • (1999) Eur. Phys. J. , vol.8 , Issue.2 , pp. 311
    • Broadhurst, D.J.1
  • 40
    • 0035981787 scopus 로고    scopus 로고
    • Nested sums, expansion of transcendental functions and multi-scale multi-loop integrals
    • S. Moch, P. Uwer and S. Weinzierl, Nested sums, expansion of transcendental functions and multi-scale multi-loop integrals 2002 J. Math. Phys. 43 3363 [hep-ph/0110083]
    • (2002) J. Math. Phys. , vol.43 , Issue.6 , pp. 3363
    • Moch, S.1    Uwer, P.2    Weinzierl, S.3
  • 41
    • 3543097016 scopus 로고    scopus 로고
    • Expansion around half-integer values, binomial sums and inverse binomial sums
    • S. Weinzierl, Expansion around half-integer values, binomial sums and inverse binomial sums 2004 J. Math. Phys. 45 2656 [hep-ph/0402131]
    • (2004) J. Math. Phys. , vol.45 , Issue.7 , pp. 2656
    • Weinzierl, S.1
  • 42
    • 5444244485 scopus 로고    scopus 로고
    • Series and -expansion of the hypergeometric functions
    • M.Y. Kalmykov, Series and -expansion of the hypergeometric functions 2004 Nucl. Phys. (Proc. Suppl.) 135 280 [hep-th/0406269]
    • (2004) Nucl. Phys. (Proc. Suppl.) , vol.135 , pp. 280
    • Kalmykov, M.Y.1
  • 43
    • 0031283601 scopus 로고    scopus 로고
    • The double logarithm and Manin's complex for modular curves
    • A.B. Goncharov, The double logarithm and Manin's complex for modular curves 1998 Math. Res. Lett. 4 (1997) 617
    • (1998) Math. Res. Lett. , vol.4
    • Goncharov, A.B.1
  • 44
    • 0032219342 scopus 로고    scopus 로고
    • Multiple polylogarithms, cyclotomy and modular complexes
    • A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes Math. Res. Lett. 5 497
    • Math. Res. Lett. , vol.5
    • Goncharov, A.B.1
  • 47
    • 0035821473 scopus 로고    scopus 로고
    • Two-loop master integrals for γ* 3 jets: The planar topologies
    • T. Gehrmann and E. Remiddi, Two-loop master integrals for γ* 3 jets: the planar topologies, 2001 Nucl. Phys. B 601 248 [hep-ph/0008287]
    • (2001) Nucl. Phys. , vol.601 , Issue.1-2 , pp. 248
    • Gehrmann, T.1    Remiddi, E.2
  • 48
    • 0002198122 scopus 로고    scopus 로고
    • Uber die Transcendeten, welche aus wiederholten Integrationen rationaler Formeln entstehen
    • E.E. Kummer, Uber die Transcendeten, welche aus wiederholten Integrationen rationaler Formeln entstehen J.reine and. Math. 21 (1840) 74
    • J.reine And. Math. , vol.21
    • Kummer, E.E.1
  • 49
    • 34250533716 scopus 로고    scopus 로고
    • Sur les Groupes des équations Linéaires
    • H. Poincaré, Sur les Groupes des équations Linéaires Acta. Math. 4 (1884) 201
    • Acta. Math. , vol.4
    • Poincaré, H.1
  • 50
    • 84856407126 scopus 로고
    • Resolution algorithmique des problèm es reguliers de Poincare et de Riemann
    • I.A. Lappo-Danilevsky, Resolution algorithmique des problèm es reguliers de Poincare et de Riemann 1928 J. Soc. Phisico-Mathematique de Leningrade 2 94
    • (1928) J. Soc. Phisico-Mathematique de Leningrade , vol.2 , pp. 94
    • Lappo-Danilevsky, I.A.1
  • 54
    • 17144365844 scopus 로고    scopus 로고
    • Explicit results for all orders of the -expansion of certain massive and massless diagrams
    • A.I. Davydychev, Explicit results for all orders of the -expansion of certain massive and massless diagrams 2000 Phys. Rev. D 61 087701 [hep-ph/9910224]
    • (2000) Phys. Rev. , vol.61 , Issue.8 , pp. 087701
    • Davydychev, A.I.1
  • 55
    • 19244381544 scopus 로고    scopus 로고
    • Some remarks on the -expansion of dimensionally regulated Feynman diagrams
    • A.I. Davydychev and M.Y. Kalmykov, Some remarks on the -expansion of dimensionally regulated Feynman diagrams 2000 Nucl. Phys. (Proc. Suppl.) 89 283 [hep-th/0005287]
    • (2000) Nucl. Phys. (Proc. Suppl.) , vol.89 , Issue.1-3 , pp. 283
    • Davydychev, A.I.1    Kalmykov, M.Y.2
  • 57
    • 33947615776 scopus 로고    scopus 로고
    • All order -expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
    • M.Y. Kalmykov, B.F.L. Ward and S. Yost, All order -expansion of Gauss hypergeometric functions with integer and half/integer values of parameters 2007 J. High Energy Phys. JHEP02(2007)040 [hep-th/0612240]
    • (2007) J. High Energy Phys. , vol.2007 , Issue.2 , pp. 040
    • Kalmykov, M.Y.1    Ward, B.F.L.2    Yost, S.3
  • 58
    • 0036664257 scopus 로고    scopus 로고
    • Very well-poised hypergeometric series and multiple integrals
    • V.V. Zudilin, Very well-poised hypergeometric series and multiple integrals 2004 Russian Math. Surveys 57 (2002) 824
    • (2004) Russian Math. Surveys , vol.57
    • Zudilin, V.V.1
  • 59
    • 4344700220 scopus 로고    scopus 로고
    • Well-poised hypergeometric transformations of Euler-type multiple integrals
    • M.Y. Kalmykov, B.F.L. Ward and S. Yost, Well-poised hypergeometric transformations of Euler-type multiple integrals J. London Math. Soc. 70 215
    • J. London Math. Soc. , vol.70 , pp. 215
    • Kalmykov, M.Y.1    Ward, B.F.L.2    Yost, S.3
  • 60
    • 0141737007 scopus 로고    scopus 로고
    • Integrals expressible as Linear Forms in generalized polylogarithms
    • S.A. Zlobin, Integrals expressible as Linear Forms in generalized polylogarithms 2005 Math. Notes 71 (2002) 711
    • (2005) Math. Notes , vol.71
    • Zlobin, S.A.1
  • 61
    • 12244268016 scopus 로고    scopus 로고
    • Decomposition of multiple integrals in linear forms
    • S.A. Zlobin, Decomposition of multiple integrals in linear forms Dokl. Akad. Nauk 398 (2004) 595
    • Dokl. Akad. Nauk , vol.398
    • Zlobin, S.A.1
  • 62
    • 21644472657 scopus 로고    scopus 로고
    • Expansion of multiple integrals in linear forms
    • S.A. Zlobin, Expansion of multiple integrals in linear forms Mat. Zametki 77 (2005) 683
    • Mat. Zametki , vol.77
    • Zlobin, S.A.1
  • 63
    • 33947536623 scopus 로고    scopus 로고
    • Properties of the coefficients of some linear forms of generalized polylogarithms
    • S.A. Zlobin, Properties of the coefficients of some linear forms of generalized polylogarithms Fundam. Prikl. Mat. 11 41
    • Fundam. Prikl. Mat. , vol.11 , pp. 41
    • Zlobin, S.A.1
  • 64
    • 35748939232 scopus 로고    scopus 로고
    • On an identity of Mahler
    • Yu.V. Nesterenko, On an identity of Mahler 2006 Mat. Zametki 79 107
    • (2006) Mat. Zametki , vol.79 , pp. 107
    • Nesterenko, Yu.V.1
  • 65
    • 35748950587 scopus 로고    scopus 로고
    • On an identity for a generalization of a hypergeometric integral
    • E.A. Ulanskii, On an identity for a generalization of a hypergeometric integral 2007 Mat. Zametki 79 (2006) 796
    • (2007) Mat. Zametki , vol.79
    • Ulanskii, E.A.1
  • 66
    • 33845788645 scopus 로고    scopus 로고
    • An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series
    • C. Krattenthaler and T. Rivoal, An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series Ramanujan J. 13 203 [math.CA/0312148]
    • Ramanujan J. , vol.13 , pp. 203
    • Krattenthaler, C.1    Rivoal, T.2
  • 68
    • 0032219840 scopus 로고    scopus 로고
    • Euler sums and contour integral representations
    • P. Flajolet and B. Salvy, Euler sums and contour integral representations 1998 Experiment. Math. 7 15
    • (1998) Experiment. Math. , vol.7
    • Flajolet, P.1    Salvy, B.2
  • 69
    • 33748294262 scopus 로고    scopus 로고
    • The two-loop vector form factor in the Sudakov limit
    • B. Jantzen and V.A. Smirnov, The two-loop vector form factor in the Sudakov limit 2006 Eur. Phys. J. C 47 671 [hep-ph/0603133]
    • (2006) Eur. Phys. J. , vol.47 , Issue.3 , pp. 671
    • Jantzen, B.1    Smirnov, V.A.2
  • 70
    • 33749327838 scopus 로고    scopus 로고
    • Planar two-loop master integrals for massive Bhabha scattering: N(f) = 1 and N(f) = 2
    • S. Actis, M. Czakon, J. Gluza and T. Riemann, Planar two-loop master integrals for massive Bhabha scattering: N(f) = 1 and N(f) = 2 2006 Nucl. Phys. (Proc. Suppl.) 160 91 [hep-ph/0609051]
    • (2006) Nucl. Phys. (Proc. Suppl.) , vol.160 , pp. 91
    • Actis, S.1    Czakon, M.2    Gluza, J.3    Riemann, T.4
  • 71
    • 0042910977 scopus 로고
    • Differential equations method: New technique for massive Feynman diagrams calculation
    • A.V. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation 1991 Phys. Lett. B 254 158
    • (1991) Phys. Lett. , vol.254 , Issue.1-2 , pp. 158
    • Kotikov, A.V.1
  • 72
    • 0542448411 scopus 로고
    • Differential equations method: The calculation of vertex type Feynman diagrams
    • A.V. Kotikov, Differential equations method: the calculation of vertex type Feynman diagrams 1991 Phys. Lett. B 259 314
    • (1991) Phys. Lett. , vol.259 , Issue.3 , pp. 314
    • Kotikov, A.V.1
  • 73
    • 0042410077 scopus 로고
    • Differential equation method: The calculation of N point Feynman diagrams
    • A.V. Kotikov, Differential equation method: the calculation of N point Feynman diagrams 1991 Phys. Lett. B 267 123
    • (1991) Phys. Lett. , vol.267 , Issue.1 , pp. 123
    • Kotikov, A.V.1
  • 74
    • 0039587439 scopus 로고
    • New method of massive Feynman diagrams calculation
    • A.V. Kotikov, New method of massive Feynman diagrams calculation 1991 Mod. Phys. Lett. A 6 677
    • (1991) Mod. Phys. Lett. , vol.6 , Issue.8 , pp. 677
    • Kotikov, A.V.1
  • 75
    • 0345870301 scopus 로고    scopus 로고
    • The differential equation method: Calculation of vertex-type diagrams with one non-zero mass
    • J. Fleischer, A.V. Kotikov and O.L. Veretin, The differential equation method: calculation of vertex-type diagrams with one non-zero mass 1998 Phys. Lett. B 417 163 [hep-ph/9707492]
    • (1998) Phys. Lett. , vol.417 , Issue.1-2 , pp. 163
    • Fleischer, J.1    Kotikov, A.V.2    Veretin, O.L.3
  • 76
    • 0013160761 scopus 로고
    • Total αs correction to deep inelastic scattering cross-section ratio, R = σl/σt in QCD. calculation of longitudinal structure function
    • t in QCD. calculation of longitudinal structure function 1988 Nucl. Phys. B 307 721 [Erratum 1990 Nucl. Phys. B 345 299]
    • (1988) Nucl. Phys. , vol.307 , Issue.4 , pp. 721
    • Kazakov, D.I.1    Kotikov, A.V.2
  • 77
    • 0001764998 scopus 로고    scopus 로고
    • Harmonic sums, Mellin transforms and integrals
    • J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals 1999 Int. J. Mod. Phys. A 14 2037 [hep-ph/9806280]
    • (1999) Int. J. Mod. Phys. , vol.14 , Issue.13 , pp. 2037
    • Vermaseren, J.A.M.1
  • 78
    • 17044378499 scopus 로고    scopus 로고
    • Harmonic sums and Mellin transforms up to two-loop order
    • J. Blumlein and S. Kurth, Harmonic sums and Mellin transforms up to two-loop order 1999 Phys. Rev. D 60 014018 [hep-ph/9810241]
    • (1999) Phys. Rev. , vol.60 , Issue.1 , pp. 014018
    • Blumlein, J.1    Kurth, S.2
  • 79
    • 5444238426 scopus 로고    scopus 로고
    • Algebraic relations between harmonic sums and associated quantities
    • J. Blumlein, Algebraic relations between harmonic sums and associated quantities 2004 Comput. Phys. Commun. 159 19 [hep-ph/0311046]
    • (2004) Comput. Phys. Commun. , vol.159 , Issue.1 , pp. 19
    • Blumlein, J.1
  • 80
    • 34547798913 scopus 로고    scopus 로고
    • Two-loop massive operator matrix elements and unpolarized heavy flavor production at asymptotic values Q2m2
    • 2 2007 Nucl. Phys. B 780 40 [hep-ph/0703285]
    • (2007) Nucl. Phys. , vol.780 , Issue.1-2 , pp. 40
    • Bierenbaum, I.1    Blumlein, J.2    Klein, S.3
  • 83
    • 33847540228 scopus 로고
    • On Nielsen's generalized polylogarithms and their numerical calculation
    • K.S. Kölbig, J.A. Mignaco and E. Remiddi, On Nielsen's generalized polylogarithms and their numerical calculation 1970 B.I.T. 10 38
    • (1970) B.I.T. , vol.10 , pp. 38
    • Kölbig, K.S.1    Mignaco, J.A.2    Remiddi, E.3
  • 84
    • 51249190659 scopus 로고
    • Electron form-factors up to fourth order. 1
    • R. Barbieri, J.A. Mignaco and E. Remiddi, Electron form-factors up to fourth order. 1 1972 Nuovo Cim. A 11 824
    • (1972) Nuovo Cim. , vol.11 , pp. 824
    • Barbieri, R.1    Mignaco, J.A.2    Remiddi, E.3
  • 85
    • 0000216244 scopus 로고
    • Nielsen's generalized polylogarithms
    • K.S. Kölbig, Nielsen's generalized polylogarithms 1986 SIAM J. Math. Anal. 17 1232
    • (1986) SIAM J. Math. Anal. , vol.17 , Issue.5 , pp. 1232
    • Kölbig, K.S.1
  • 86
    • 0034289358 scopus 로고    scopus 로고
    • Special functions of the isomonodromy type
    • A.V. Kitaev, Special functions of the isomonodromy type 2000 Acta Appl. Math. 64 1
    • (2000) Acta Appl. Math. , vol.64 , Issue.1 , pp. 1
    • Kitaev, A.V.1
  • 91
    • 25144484308 scopus 로고    scopus 로고
    • Lsjk: A C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions
    • M.Y. Kalmykov and A. Sheplyakov, lsjk: a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions 2005 Comput. Phys. Commun. 172 45 [hep-ph/0411100]
    • (2005) Comput. Phys. Commun. , vol.172 , Issue.1 , pp. 45
    • Kalmykov, M.Y.1    Sheplyakov, A.2
  • 93
    • 0010861998 scopus 로고
    • The algebra of linear partial difference operators and its applications
    • D. Zeilberger, The algebra of linear partial difference operators and its applications 1980 SIAM J. Math. Anal. 11 919
    • (1980) SIAM J. Math. Anal. , vol.11
    • Zeilberger, D.1
  • 94
    • 0000089705 scopus 로고
    • Gröbner basis and the problem of contiguous relations
    • N. Takayama, Gröbner basis and the problem of contiguous relations 1989 Japan J. Appl. Math. 6 147
    • (1989) Japan J. Appl. Math. , vol.6
    • Takayama, N.1
  • 96
    • 84856390301 scopus 로고    scopus 로고
    • see also http://www-zeuthen.desy.de/riemann/Talks/riemann-zif-07.pdf
  • 98
    • 0007128860 scopus 로고    scopus 로고
    • A class of series acceleration formulae for Catalan's constant
    • D.M. Bradley, A class of series acceleration formulae for Catalan's constant 1999 Ramanujan J. 3 159 [0706.0356]
    • (1999) Ramanujan J. , vol.3 , Issue.2 , pp. 159
    • Bradley, D.M.1
  • 99
    • 0033243811 scopus 로고    scopus 로고
    • Borwein and Bradley's Apéry-like formulae for ζ(4n+3)
    • G. Almkvist and A. Granville, Borwein and Bradley's Apéry-like formulae for ζ(4n+3) 1999 Experiment. Math. 8 197
    • (1999) Experiment. Math. , vol.8 , pp. 197
    • Almkvist, G.1    Granville, A.2
  • 100
    • 14944361601 scopus 로고    scopus 로고
    • Simultaneous generation of Koecher and Almkvist-Granville's Apéry-like formulae
    • T. Rivoal, Simultaneous generation of Koecher and Almkvist-Granville's Apéry-like formulae 2004 Experiment. Math. 13 503
    • (2004) Experiment. Math. , vol.13
    • Rivoal, T.1
  • 102
    • 33750875429 scopus 로고    scopus 로고
    • Experimental determination of Apéry-like identities for ζ(2n+2)
    • D. Bailey, J.M. Borwein and D.M. Bradley, Experimental determination of Apéry-like identities for ζ(2n+2) 2006 Experiment. Math. 15 281 [math/0505270]
    • (2006) Experiment. Math. , vol.15
    • Bailey, D.1    Borwein, J.M.2    Bradley, D.M.3
  • 103
    • 0038932650 scopus 로고    scopus 로고
    • Analysis of PSLQ, an integer relation finding algorithm
    • H.R.P. Ferguson, D.H. Bailey and S. Arno, Analysis of PSLQ, an integer relation finding algorithm 2001 Math. Comp. 68 (1999) 351
    • (2001) Math. Comp. , vol.68
    • Ferguson, H.R.P.1    Bailey, D.H.2    Arno, S.3
  • 104
    • 0035595042 scopus 로고    scopus 로고
    • Parallel integer relation detection: Techniques and applications
    • D.H. Bailey and D. Broadhurst, Parallel integer relation detection: techniques and applications Math. Comp. 70 1719
    • Math. Comp. , vol.70
    • Bailey, D.H.1    Broadhurst, D.2
  • 105
    • 0035633684 scopus 로고    scopus 로고
    • Central binomial sums, multiple clausen values and zeta values
    • J.M. Borwein, D.J. Broadhurst and J. Kamnitzer, Central binomial sums, multiple clausen values and zeta values 2001 Exper. Math. 10 25 [hep-th/0004153]
    • (2001) Exper. Math. , vol.10 , pp. 25
    • Borwein, J.M.1    Broadhurst, D.J.2    Kamnitzer, J.3
  • 107
    • 20044379808 scopus 로고    scopus 로고
    • About higher order -expansion of some massive two- and three-loop master-integrals
    • M.Y. Kalmykov, About higher order -expansion of some massive two- and three-loop master-integrals 2005 Nucl. Phys. B 718 276 [hep-ph/0503070]
    • (2005) Nucl. Phys. , vol.718 , Issue.1-2 , pp. 276
    • Kalmykov, M.Y.1
  • 108
    • 0001572516 scopus 로고    scopus 로고
    • Two-loop self-energy master integrals on shell
    • J. Fleischer, M.Y. Kalmykov and A.V. Kotikov, Two-loop self-energy master integrals on shell 1999 Phys. Lett. B 462 169 [Erratum 1999 Phys. Lett. B 467 310] [hep-ph/9905249]
    • (1999) Phys. Lett. , vol.462 , Issue.1-2 , pp. 169
    • Fleischer, J.1    Kalmykov, M.Y.2    Kotikov, A.V.3
  • 109
    • 0034205201 scopus 로고    scopus 로고
    • ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the standard model
    • J. Fleischer and M.Y. Kalmykov, ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the standard model 2000 Comput. Phys. Commun. 128 531 [hep-ph/9907431]
    • (2000) Comput. Phys. Commun. , vol.128 , Issue.3 , pp. 531
    • Fleischer, J.1    Kalmykov, M.Y.2
  • 110
    • 0033576458 scopus 로고    scopus 로고
    • Single mass scale diagrams: Construction of a basis for the -expansion
    • J. Fleischer and M.Y. Kalmykov, Single mass scale diagrams: construction of a basis for the -expansion 1999 Phys. Lett. B 470 168 [hep-ph/9910223]
    • (1999) Phys. Lett. , vol.470 , Issue.1-4 , pp. 168
    • Fleischer, J.1    Kalmykov, M.Y.2
  • 111
    • 17044374650 scopus 로고    scopus 로고
    • Numerical evaluation of multiple polylogarithms
    • J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms 2005 Comput. Phys. Commun. 167 177 [hep-ph/0410259]
    • (2005) Comput. Phys. Commun. , vol.167 , Issue.3 , pp. 177
    • Vollinga, J.1    Weinzierl, S.2
  • 114
    • 5444234143 scopus 로고    scopus 로고
    • Algebraic relations for multiple zeta values
    • V.V. Zudilin, Algebraic relations for multiple zeta values 2003 Russian Math. Surveys 58 1
    • (2003) Russian Math. Surveys , vol.58
    • Zudilin, V.V.1
  • 115
    • 0001141766 scopus 로고
    • Algebras of iterated path integrals and fundamental groups
    • K.T. Chen, Algebras of iterated path integrals and fundamental groups 1971 Trans. Am. Math. Soc. 156 359
    • (1971) Trans. Am. Math. Soc. , vol.156 , pp. 359
    • Chen, K.T.1


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