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Volumn 41, Issue 20, 2008, Pages

Elliptic integral evaluations of Bessel moments and applications

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EID: 44649120453     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/20/205203     Document Type: Article
Times cited : (152)

References (77)
  • 2
    • 2342436635 scopus 로고
    • The evaluation of integrals of Bessel functions via G-function identities
    • Adamchik V 1995 The evaluation of integrals of Bessel functions via G-function identities J. Comput. Appl. Math 64 283-90
    • (1995) J. Comput. Appl. Math , vol.64 , Issue.3 , pp. 283-290
    • Adamchik, V.1
  • 3
    • 0001484410 scopus 로고
    • Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the ladies diary
    • Almkvist Gert and Berndt Bruce 1988 Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the ladies diary Am. Math. Mon. 95 585-608
    • (1988) Am. Math. Mon. , vol.95 , Issue.7 , pp. 585-608
    • Gert, A.1    Bruce, B.2
  • 5
    • 0003951026 scopus 로고    scopus 로고
    • Integer relation detection
    • Bailey David H 2000 Integer relation detection Comput. Sci. Eng. 24-8
    • (2000) Comput. Sci. Eng. , vol.2 , Issue.1 , pp. 24-28
    • Bailey David, H.1
  • 6
    • 44649086717 scopus 로고    scopus 로고
    • Highly parallel, high-precision numerical integration
    • Bailey David H and Borwein Jonathan M 2006 Highly parallel, high-precision numerical integration Int. J. Comp. Sci. Eng. (at press) http://crd.lbl.gov/∼dhbailey/dhbpapers/quadparallel.pdf
    • (2006) Int. J. Comp. Sci. Eng.
    • Bailey David, H.1    Borwein Jonathan, M.2
  • 10
    • 38549179750 scopus 로고    scopus 로고
    • Hypergeometric forms for Ising-class integrals
    • Bailey David H, Borwein David, Borwein Jonathan M and Crandall Richard 2007 Hypergeometric forms for Ising-class integrals Exp. Math. 16 257-76 http://crd.lbl.gov/∼dhbailey/dhbpapers/meijer.pdf
    • (2007) Exp. Math. , vol.16 , pp. 257-276
    • Bailey David, H.1    David, B.2    Borwein Jonathan, M.3    Richard, C.4
  • 12
    • 0035595042 scopus 로고    scopus 로고
    • Parallel integer relation detection: Techniques and applications
    • Bailey David H and Broadhurst David J 2001 Parallel integer relation detection: techniques and applications Math. Comp. 70 1719-1736 http://crd.lbl.gov/∼dhbailey/dhbpapers/ppslq.pdf
    • (2001) Math. Comp. , vol.70 , Issue.236 , pp. 1719-1736
    • Bailey David, H.1    Broadhurst David, J.2
  • 14
    • 27844549343 scopus 로고    scopus 로고
    • A comparison of three high-precision quadrature schemes
    • Bailey David H, Li Xiaoye S and Jeyabalan Karthik 2005 A comparison of three high-precision quadrature schemes Exp. Math. 14 317-29 http://crd.lbl.gov/∼dhbailey/dhbpapers/quadrature.pdf
    • (2005) Exp. Math. , vol.14 , pp. 317-329
    • Bailey David, H.1    Li Xiaoye, S.2    Karthik, J.3
  • 16
    • 84963082052 scopus 로고
    • Some infinite integrals involving Bessel functions
    • Bailey W N 1936 Some infinite integrals involving Bessel functions Proc. Lond. Math. Soc. 40 37-48
    • (1936) Proc. Lond. Math. Soc. , vol.2-40 , Issue.1 , pp. 37-48
    • Bailey, W.N.1
  • 17
    • 84960555218 scopus 로고
    • Some infinite integrals involving Bessel functions: II
    • Bailey W N 1936 Some infinite integrals involving Bessel functions: II J. Lond. Math. Soc. 11 16-20
    • (1936) J. Lond. Math. Soc. , vol.1-11 , Issue.1 , pp. 16-20
    • Bailey, W.N.1
  • 18
    • 44649086716 scopus 로고
    • A combinatorial identity (Problem 75-4)
    • Barrucand P 1975 A combinatorial identity (Problem 75-4) SIAM Rev. 17 168
    • (1975) SIAM Rev. , vol.17 , Issue.1 , pp. 168
    • Barrucand, P.1
  • 21
    • 36149035792 scopus 로고
    • Lattice magnetic walks
    • Blum T and Shapir Y 1994 Lattice magnetic walks J. Phys. A: Math. Gen. 27 295-315 http://arxiv.org/PS_cache/cond-mat/pdf/9310/9310024v1.pdf
    • (1994) J. Phys. A: Math. Gen. , vol.27 , Issue.2 , pp. 295-315
    • Blum, T.1    Shapir, Y.2
  • 27
    • 44649149875 scopus 로고    scopus 로고
    • A proof of a recursion for Bessel moments
    • Borwein Jonathan and Salvy Bruno 2007 A proof of a recursion for Bessel moments Exp. Math. http://locutus.cs.dal.ca:8088/archive/00000346/ (at press)
    • (2007) Exp. Math.
    • Jonathan, B.1    Bruno, S.2
  • 29
    • 34249959481 scopus 로고
    • The master two-loop diagram with masses
    • Broadhurst D J 1990 The master two-loop diagram with masses Z. Phys. C 47 115-24
    • (1990) Z. Phys. , vol.47 , Issue.1 , pp. 115-124
    • Broadhurst, D.J.1
  • 30
    • 0000377345 scopus 로고    scopus 로고
    • Massive three-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity
    • Broadhurst D J 1999 Massive three-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity Eur. Phys. J. C 8 311-33 http://arxiv.org/PS_cache/hep-th/pdf/9803/9803091v1.pdf
    • (1999) Eur. Phys. J. , vol.8 , Issue.2 , pp. 311-333
    • Broadhurst, D.J.1
  • 31
    • 0003061686 scopus 로고
    • Two-loop two-point functions with masses: Asymptotic expansions and Taylor series
    • Broadhurst D J, Fleischer J and Tarasov O V 1993 Two-loop two-point functions with masses: Asymptotic expansions and Taylor series Z. Phys. C 60 287-302 (in any dimension) http://arxiv.org/PS_cache/hep-ph/pdf/9304/9304303v1. pdf
    • (1993) Z. Phys. , vol.60 , Issue.2 , pp. 287-302
    • Broadhurst, D.J.1    Fleischer, J.2    Tarasov, O.V.3
  • 32
    • 36149012581 scopus 로고
    • Some applications of the generalized unitarity relation
    • Cutkosky R E 1960 Some applications of the generalized unitarity relation Phys. Rev. Lett. 4 624-6
    • (1960) Phys. Rev. Lett. , vol.4 , Issue.12 , pp. 624-626
    • Cutkosky, R.E.1
  • 33
    • 29744468057 scopus 로고
    • Singularities and discontinuities of Feynman amplitudes
    • Cutkosky R E 1960 Singularities and discontinuities of Feynman amplitudes J. Math. Phys. 1 429-33
    • (1960) J. Math. Phys. , vol.1 , Issue.5 , pp. 429-433
    • Cutkosky, R.E.1
  • 35
    • 2442487606 scopus 로고    scopus 로고
    • Explicitly symmetrical treatment of three body phase space
    • Davydychev A I and Delbourgo R 2004 Explicitly symmetrical treatment of three body phase space J. Phys. A: Math. Gen. 37 4871-86 http://arxiv.org/ PS_cache/hep-th/pdf/0311/0311075v1.pdf
    • (2004) J. Phys. A: Math. Gen. , vol.37 , Issue.17 , pp. 4871-4886
    • Davydychev, A.I.1    Delbourgo, R.2
  • 36
    • 0000776807 scopus 로고
    • Two-loop self-energy diagrams with different masses and the momentum expansion
    • Davydychev A I and Tausk J B 1993 Two-loop self-energy diagrams with different masses and the momentum expansion Nucl. Phys. B 397 123-42 http://www.higgs.de/∼davyd/papers/dt1.pdf
    • (1993) Nucl. Phys. , vol.397 , Issue.1-2 , pp. 123-142
    • Davydychev, A.I.1    Tausk, J.B.2
  • 37
    • 0001677138 scopus 로고    scopus 로고
    • A magic connection between massive and massless diagrams
    • Davydychev A I and Tausk J B 1996 A magic connection between massive and massless diagrams Phys. Rev. D 53 7381-7384 http://arxiv.org/PS_cache/hep-ph/ pdf/9504/9504431v1.pdf
    • (1996) Phys. Rev. , vol.53 , Issue.12 , pp. 7381-7384
    • Davydychev, A.I.1    Tausk, J.B.2
  • 38
    • 84945612853 scopus 로고
    • On the theory of cooperative phenomena in crystals
    • Domb C 1960 On the theory of cooperative phenomena in crystals Adv. Phys. 9 149-361
    • (1960) Adv. Phys. , vol.9 , Issue.35 , pp. 245-361
    • Domb, C.1
  • 40
    • 0007112977 scopus 로고
    • Definite integrals of the complete elliptic integral K
    • Glasser M L 1976 Definite integrals of the complete elliptic integral K J. Res. NBS 80B 313-23
    • (1976) J. Res. NBS , vol.80 , pp. 313-323
    • Glasser, M.L.1
  • 41
    • 44649113362 scopus 로고    scopus 로고
    • A two-parameter generalization of the complete elliptic integral of the second kind
    • Glasser M L 2007 A two-parameter generalization of the complete elliptic integral of the second kind HAIT J. Sci. Eng. A http://arxiv.org/PS_cache/arxiv/ pdf/0709/0709.1289v1.pdf (at press)
    • (2007) HAIT J. Sci. Eng.
    • Glasser, M.L.1
  • 43
    • 34548058409 scopus 로고    scopus 로고
    • On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
    • Groote S, Korner J G and Pivovarov A A 2007 On the evaluation of a certain class of Feynman diagrams in x-space: sunrise-type topologies at any loop order Ann. Phys. 322 2374-445 http://arxiv.org/PS_cache/hep-ph/pdf/0506/ 0506286v1.pdf
    • (2007) Ann. Phys. , vol.322 , Issue.10 , pp. 2374-2445
    • Groote, S.1    Korner, J.G.2    Pivovarov, A.A.3
  • 44
    • 0011630495 scopus 로고
    • Staircase polygons, elliptic integrals, Heun functions and lattice Green functions
    • Guttmann A J and Prellberg T 1993 Staircase polygons, elliptic integrals, Heun functions and lattice Green functions Phys. Rev. E 47 2233-2236
    • (1993) Phys. Rev. , vol.47 , Issue.4 , pp. 2233-2236
    • Guttmann, A.J.1    Prellberg, T.2
  • 45
    • 84963486931 scopus 로고
    • On the enumeration of rectangular (0,1)-matrices
    • Hendrickson J A Jr 1995 On the enumeration of rectangular (0,1)-matrices J. Stat. Comput. Simul. 51 291-313
    • (1995) J. Stat. Comput. Simul. , vol.51 , Issue.2 , pp. 291-313
    • Hendrickson, J.A.1
  • 46
    • 33745594810 scopus 로고    scopus 로고
    • Lattice Green's function for the diamond lattice
    • Hijjawi R S 2006 Lattice Green's function for the diamond lattice Int. J. Theor. Phys. 45 135-46
    • (2006) Int. J. Theor. Phys. , vol.45 , Issue.1 , pp. 129-146
    • Hijjawi, R.S.1
  • 47
    • 36149017953 scopus 로고
    • Distribution of recoil nucleus in pair production by photons
    • Jost R, Luttinger J M and Slotnick M 1950 Distribution of recoil nucleus in pair production by photons Phys. Rev. 80 189-196
    • (1950) Phys. Rev. , vol.80 , Issue.2 , pp. 189-196
    • Jost, R.1    Luttinger, J.M.2    Slotnick, M.3
  • 48
    • 18744392927 scopus 로고
    • Lattice Green function for the anisotropic face centred cubic lattice
    • Joyce G S 1971 Lattice Green function for the anisotropic face centred cubic lattice J. Phys. 4 L53-6
    • (1971) J. Phys. , vol.4
    • Joyce, G.S.1
  • 49
    • 0141691780 scopus 로고
    • Exact evaluation of the body centred cubic lattice Green function
    • Joyce G S 1971 Exact evaluation of the body centred cubic lattice Green function J. Phys. 4 1510-2
    • (1971) J. Phys. , vol.4 , pp. 1510-1512
    • Joyce, G.S.1
  • 52
    • 12744278692 scopus 로고    scopus 로고
    • On the evaluation of generalized Watson integrals
    • Joyce G S and Zucker I J 2004 On the evaluation of generalized Watson integrals Proc. Am. Math. Soc. 133 71-81
    • (2004) Proc. Am. Math. Soc. , vol.133 , Issue.1 , pp. 71-81
    • Joyce, G.S.1    Zucker, I.J.2
  • 57
    • 0034736523 scopus 로고    scopus 로고
    • High precision calculation of multiloop Feynman integrals by difference equations
    • Laporta S 2000 High precision calculation of multiloop Feynman integrals by difference equations Int. J. Mod. Phys. A 15 5087-159 http://arxiv.org/ PS_cache/hep-ph/pdf/0102/0102033v1.pdf
    • (2000) Int. J. Mod. Phys. , vol.15 , Issue.32 , pp. 5087-5159
    • Laporta, S.1
  • 58
    • 0037191827 scopus 로고    scopus 로고
    • High precision epsilon expansions of massive four loop vacuum bubbles
    • Laporta S 2002 High precision epsilon expansions of massive four loop vacuum bubbles Phys. Lett. B 549 115-22 http://arxiv.org/PS_cache/hep-ph/pdf/ 0210/0210336v1.pdf
    • (2002) Phys. Lett. , vol.549 , Issue.1-2 , pp. 115-122
    • Laporta, S.1
  • 62
    • 26244457747 scopus 로고    scopus 로고
    • Random Aharonov-bohm vortices and some exactly solvable families of integrals
    • Ouvry Stephane 2005 Random Aharonov-bohm vortices and some exactly solvable families of integrals J. Stat. Mech.: Theory Exp. 1 P09004 (Preprint cond-mat/0502366)
    • (2005) J. Stat. Mech.: Theory Exp. , vol.1 , pp. 09004
    • Stephane, O.1
  • 63
    • 34247635087 scopus 로고    scopus 로고
    • Multi-parton cross sections at hadron colliders
    • Papadopoulos C G and Worek M 2007 Multi-parton cross sections at hadron colliders Eur. Phys. J. C 50 843-56 http://arxiv.org/PS_cache/hep-ph/pdf/0512/ 0512150v2.pdf
    • (2007) Eur. Phys. J. , vol.50 , Issue.4 , pp. 843-856
    • Papadopoulos, C.G.1    Worek, M.2
  • 67
    • 0000787181 scopus 로고
    • Fourth order spectral functions for the electron propagator
    • Sabry A 1962 Fourth order spectral functions for the electron propagator Nucl. Phys. 33 401-30
    • (1962) Nucl. Phys. , vol.33 , pp. 401-430
    • Sabry, A.1
  • 69
  • 73
    • 0000003432 scopus 로고
    • S-Matrix and causality condition: I. Maxwell field
    • van Kampen N G 1953 S-Matrix and causality condition: I. Maxwell field Phys. Rev. 89 1072-1079
    • (1953) Phys. Rev. , vol.89 , Issue.5 , pp. 1072-1079
    • Van Kampen, N.G.1
  • 74
    • 36149020037 scopus 로고
    • S-Matrix and causality condition: II. Nonrelativistic particles
    • van Kampen N G 1953 S-Matrix and causality condition: II. Nonrelativistic particles Phys. Rev. 91 1267-1276
    • (1953) Phys. Rev. , vol.91 , Issue.5 , pp. 1267-1276
    • Van Kampen, N.G.1
  • 75
    • 0001669445 scopus 로고
    • Linked-cluster expansion for quantum spin systems and the perpendicular susceptibility of the Ising model
    • Wang Yung-Li, Wentworth Chris and Westwanski B 1985 Linked-cluster expansion for quantum spin systems and the perpendicular susceptibility of the Ising model Phys. Rev. B 32 1805-1812
    • (1985) Phys. Rev. , vol.32 , Issue.3 , pp. 1805-1812
    • Yung-Li, W.1    Chris, W.2    Westwanski, B.3
  • 76
    • 77957289671 scopus 로고
    • Three triple integrals
    • Watson G N 1939 Three triple integrals Q. J. Math. (Oxford) 10 266-76
    • (1939) Q. J. Math. (Oxford) , vol.10 , Issue.1 , pp. 266-276
    • Watson, G.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.