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Volumn 2007, Issue 2, 2007, Pages

All order ε-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters

Author keywords

Differential and algebraic geometry; NLO computations

Indexed keywords


EID: 33947615776     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/02/040     Document Type: Article
Times cited : (39)

References (81)
  • 3
    • 33749008637 scopus 로고
    • A method of evaluating massive Feynman integrals
    • E.E. Boos, A.I. Davydychev, A method of evaluating massive Feynman integrals 1991 Theor. Math. Phys. 89 1052
    • (1991) Theor. Math. Phys. , vol.89 , Issue.1 , pp. 1052
    • Boos, E.E.1    Davydychev, A.I.2
  • 4
    • 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
  • 5
    • 34748819382 scopus 로고
    • General results for massive N point Feynman diagrams with different masses
    • N.N. Bogoliubov, D.V. Shirkov, 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
    • Bogoliubov, N.N.1    Shirkov, D.V.2
  • 6
    • 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
  • 7
    • 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
  • 8
    • 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
  • 9
    • 0000781288 scopus 로고
    • Analytical and numerical methods for massive two loop selfenergy diagrams
    • S. Bauberger, F.A. Berends, M. Böhm and M. Buza, Analytical and numerical methods for massive two loop selfenergy diagrams 1995 Nucl. Phys. B 434 383 [hep-ph/9409388]
    • (1995) Nucl. Phys. , vol.434 , Issue.1-2 , pp. 383
    • Bauberger, S.1    Berends, F.A.2    Böhm, M.3    Buza, M.4
  • 10
    • 17144411516 scopus 로고    scopus 로고
    • Effect of Mc on b quark chromomagnetic interaction and on-shell two-loop integrals with two masses
    • 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
  • 11
    • 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
  • 12
    • 0037433828 scopus 로고    scopus 로고
    • MS-bar vs pole masses of gauge bosons. II: Two-loop electroweak fermion corrections
    • F. Jegerlehner, M.Y. Kalmykov and O. Veretin, MS-bar 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
  • 13
    • 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
  • 14
    • 33749995609 scopus 로고
    • Negative dimensional integrals. 1. Feynman graphs
    • I.G. Halliday and R.M. Ricotta, Negative dimensional integrals. 1. Feynman graphs 1987 Phys. Lett. B 193 241
    • (1987) Phys. Lett. , vol.193 , Issue.2-3 , pp. 241
    • Halliday, I.G.1    Ricotta, R.M.2
  • 15
    • 0034678179 scopus 로고    scopus 로고
    • Scalar one-loop integrals using the negative-dimension approach
    • C. Anastasiou, E.W.N. Glover and C. Oleari, Scalar one-loop integrals using the negative-dimension approach 2000 Nucl. Phys. B 572 307 [hep-ph/9907494]
    • (2000) Nucl. Phys. , vol.572 , Issue.1-2 , pp. 307
    • Anastasiou, C.1    Glover, E.W.N.2    Oleari, C.3
  • 16
    • 0034676932 scopus 로고    scopus 로고
    • Application of the negative-dimension approach to massless scalar box integrals
    • C. Anastasiou, E.W.N. Glover and C. Oleari, Application of the negative-dimension approach to massless scalar box integrals 2000 Nucl. Phys. B 565 445 [hep-ph/9907523]
    • (2000) Nucl. Phys. , vol.565 , Issue.1-2 , pp. 445
    • Anastasiou, C.1    Glover, E.W.N.2    Oleari, C.3
  • 17
    • 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
  • 18
    • 84981893403 scopus 로고
    • Mathematical foundations of the dimensional method
    • G. Rufa, Mathematical foundations of the dimensional method 1990 Annalen Phys. 47 6
    • (1990) Annalen Phys. , vol.47 , pp. 6
    • Rufa, G.1
  • 19
    • 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
  • 20
    • 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
  • 21
    • 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
  • 22
    • 0040054123 scopus 로고    scopus 로고
    • Differential equations for Feynman graph amplitudes
    • E. Remiddi, Differential equations for Feynman graph amplitudes 1997 Nuovo Cim. A 110 1435 [hep-th/9711188]
    • (1997) Nuovo Cim. , vol.110 , pp. 1435
    • Remiddi, E.1
  • 23
    • 0034288905 scopus 로고    scopus 로고
    • Application and explicit solution of recurrence relations with respect to space-time dimension
    • O.V. Tarasov, Application and explicit solution of recurrence relations with respect to space-time dimension 2000 Nucl. Phys. (Proc. Suppl.) 89 237 [hep-ph/0102271]
    • (2000) Nucl. Phys. (Proc. Suppl.) , vol.89 , Issue.1-3 , pp. 237
    • Tarasov, O.V.1
  • 24
    • 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
  • 25
    • 4243554818 scopus 로고
    • Loop integrals, R functions and their analytic continuation
    • L. Brucher, J. Franzkowski and D. Kreimer, Loop integrals, R functions and their analytic continuation 1994 Mod. Phys. Lett. A 9 2335 [hep-th/9307055]
    • (1994) Mod. Phys. Lett. , vol.9 , Issue.25 , pp. 2335
    • Brucher, L.1    Franzkowski, J.2    Kreimer, D.3
  • 26
    • 33644959490 scopus 로고    scopus 로고
    • Geometrical methods in loop calculations and the three-point function
    • A.I. Davydychev, Geometrical methods in loop calculations and the three-point function 2006 Nucl. Instrum. Meth. A 559 293 [hep-th/0509233]
    • (2006) Nucl. Instrum. Meth. , vol.559 , Issue.1 , pp. 293
    • Davydychev, A.I.1
  • 27
    • 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
  • 28
    • 0010806732 scopus 로고
    • Three loop on-shell charge renormalization without integration: Lambda-MS (QED) to four loops
    • D.J. Broadhurst, Three loop on-shell charge renormalization without integration: Lambda-MS (QED) to four loops 1992 Z. Physik C 54 599
    • (1992) Z. Physik , vol.54 , Issue.4 , pp. 599
    • Broadhurst, D.J.1
  • 29
    • 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 [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
  • 30
    • 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
  • 31
    • 33748180606 scopus 로고    scopus 로고
    • Master integrals for massless three-loop form factors: One-loop and two-loop insertions
    • T. Gehrmann, G. Heinrich, T. Huber and C. Studerus, Master integrals for massless three-loop form factors: one-loop and two-loop insertions 2006 Phys. Lett. B 640 252 [hep-ph/0607185]
    • (2006) Phys. Lett. , vol.640 , Issue.5-6 , pp. 252
    • Gehrmann, T.1    Heinrich, G.2    Huber, T.3    Studerus, C.4
  • 32
    • 33749346384 scopus 로고    scopus 로고
    • Hypergeometric representation of a four-loop vacuum bubble
    • E. Bejdakic and Y. Schroder, 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    Schroder, Y.2
  • 33
    • 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 1997 Math. Res. Lett. 4 617
    • (1997) Math. Res. Lett. , vol.4 , pp. 617
    • Goncharov, A.B.1
  • 34
    • 0032219342 scopus 로고    scopus 로고
    • Multiple polylogarithms, cyclotomy and modular complexes
    • A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes 1998 Math. Res. Lett. 5 497.
    • (1998) Math. Res. Lett. , vol.5 , pp. 497
    • Goncharov, A.B.1
  • 35
    • 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
  • 37
    • 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
  • 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
    • 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
  • 42
    • 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
  • 43
    • 5444244485 scopus 로고    scopus 로고
    • Series and epsilon-expansion of the hypergeometric functions
    • M.Y. Kalmykov, Series and epsilon-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
  • 44
    • 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
  • 49
    • 0041073087 scopus 로고
    • The three-term recurrence relation and the differentiation formulas for hypergeometric-type functions
    • R.J. Yãez, J.S. Dehesa, A.F. Nikiforov, The three-term recurrence relation and the differentiation formulas for hypergeometric-type functions 1994 J. Math. Anal. Appl. 188 855
    • (1994) J. Math. Anal. Appl. , vol.188 , Issue.3 , pp. 855
    • Yãez, R.J.1    Dehesa, J.S.2    Nikiforov, A.F.3
  • 50
    • 0035151566 scopus 로고    scopus 로고
    • Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems
    • E.J. Weniger, Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems 2001 Comput. Phys. Comm. 133 202
    • (2001) Comput. Phys. Comm. , vol.133 , Issue.2-3 , pp. 202
    • Weniger, E.J.1
  • 51
    • 0037380158 scopus 로고    scopus 로고
    • Contiguous relations of hypergeometric series
    • R. Vidunas, Contiguous relations of hypergeometric series 2003 J. Comput. Applied Math. 153 507 [math.CA/0109222]
    • (2003) J. Comput. Applied Math. , vol.153 , Issue.1-2 , pp. 507
    • Vidunas, R.1
  • 53
    • 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
  • 55
    • 33748744827 scopus 로고    scopus 로고
    • Chen's iterated integral represents the operator product expansion
    • D. Kreimer, Chen's iterated integral represents the operator product expansion 2000 Adv. Theor. Math. Phys. 3 3 [hep-th/9901099]
    • (2000) Adv. Theor. Math. Phys. , vol.3 , pp. 3
    • Kreimer, D.1
  • 57
    • 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
  • 58
    • 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
  • 59
    • 0000216244 scopus 로고
    • Nielsen's generalized polylogarithms
    • K.S. Kölbig, Nielsen's generalized polylogarithms1986 Siam J. Math. Anal. 17 1232
    • (1986) Siam J. Math. Anal. , vol.17 , Issue.5 , pp. 1232
    • Kölbig, K.S.1
  • 60
    • 33745219429 scopus 로고    scopus 로고
    • Hypexp, a mathematica package for expanding hypergeometric functions around integer-valued parameters
    • T. Huber and D. Maitre, Hypexp, a mathematica package for expanding hypergeometric functions around integer-valued parameters 2006 Comput. Phys. Commun. 175 122 [hep-ph/0507094]
    • (2006) Comput. Phys. Commun. , vol.175 , Issue.2 , pp. 122
    • Huber, T.1    Maitre, D.2
  • 63
    • 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
  • 64
    • 0037186218 scopus 로고    scopus 로고
    • Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables
    • M. Bigotte, G. Jacob, N.E. Oussous, M. Petitot, Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables 2002 Theoret. Comput. Sci. 273 271
    • (2002) Theoret. Comput. Sci. , vol.273 , Issue.1-2 , pp. 271
    • Bigotte, M.1    Jacob, G.2    Oussous, N.E.3    Petitot, M.4
  • 65
    • 5444237086 scopus 로고    scopus 로고
    • Shuffle algebra and differential galois group of colored polylogarithms
    • N.-M. Hoang, Shuffle algebra and differential galois group of colored polylogarithms 2004 Nucl. Phys. (Proc. Suppl.) 135 220
    • (2004) Nucl. Phys. (Proc. Suppl.) , vol.135 , pp. 220
    • Hoang, N.-M.1
  • 66
    • 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
  • 67
    • 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
  • 68
    • 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
  • 69
    • 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
  • 71
    • 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
  • 72
    • 33947660031 scopus 로고    scopus 로고
    • Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
    • C. Anastasiou, S. Beerli, S. Bucherer, A. Daleo and Z. Kunszt, Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop 2007 J. High Energy Phys. JHEP01(2007)082 [hep-ph/0611236]
    • (2007) J. High Energy Phys. , vol.2007 , Issue.1 , pp. 082
    • Anastasiou, C.1    Beerli, S.2    Bucherer, S.3    Daleo, A.4    Kunszt, Z.5
  • 73
    • 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
  • 74
    • 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
    • Borwein, J.M.1    Broadhurst, D.J.2    Kamnitzer, J.3
  • 76
    • 0347755140 scopus 로고    scopus 로고
    • Identities for generalized polylogarithms
    • E.A. Ulanskii, Identities for generalized polylogarithms 2003 Math. Notes 73 571
    • (2003) Math. Notes , vol.73 , pp. 571
    • Ulanskii, E.A.1
  • 77
    • 4544306639 scopus 로고    scopus 로고
    • Relations for multiple zeta values and Mellin transforms of multiple polylogarithms
    • J. Okuda, K. Ueno, Relations for multiple zeta values and Mellin transforms of multiple polylogarithms 2004 Publ. Res. Inst. Math. Sci. 40 537
    • (2004) Publ. Res. Inst. Math. Sci. , vol.40 , Issue.2 , pp. 537
    • Okuda, J.1    Ueno, K.2
  • 78
    • 0031571558 scopus 로고    scopus 로고
    • The algebra of multiple harmonic series
    • M.E. Hoffman, The algebra of multiple harmonic series 1997 J. Algebra 194 477
    • (1997) J. Algebra , vol.194 , Issue.2 , pp. 477
    • Hoffman, M.E.1
  • 79
    • 0003143654 scopus 로고    scopus 로고
    • A generalization of the duality and sum formulas on the multiple zeta values
    • Y. Ohno, A generalization of the duality and sum formulas on the multiple zeta values 1999 J. Number Th. 74 39
    • (1999) J. Number Th. , vol.74 , Issue.1 , pp. 39
    • Ohno, Y.1
  • 80
    • 33947677118 scopus 로고    scopus 로고
    • http://theor.jinr.ru/∼kalmykov/hypergeom/hyper.html
  • 81
    • 33947633267 scopus 로고    scopus 로고
    • http://www.pims.math.ca/science/2006/06motives/


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.