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We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics.
R. de L. Kronig, “On the theory of the dispersion of X-rays,”
1926
Earlier work this paper cites.
H.A. Kramers, “La diffusion de la lumière par les atomes,”
1927
Earlier work this paper cites.
W. N. Bailey,
1935
Earlier work this paper cites.
W. N. Bailey, “Some infinite integrals involving Bessel functions,”
1936
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W. N. Bailey, “Some infinite integrals involving Bessel functions (II),”
1936
Earlier work this paper cites.
F.G. Tricomi,
1936
Earlier work this paper cites.
G.N. Watson, “Three triple integrals,”
1939
Earlier work this paper cites.
G.N. Watson,
1944
Earlier work this paper cites.
R. Jost, J.M. Luttinger and M. Slotnick, “Distribution of recoil nucleus in pair production by photons,”
1950
Earlier work this paper cites.
A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi,
1953
Earlier work this paper cites.
N.G. van Kampen, “S-Matrix and causality condition. I. Maxwell field”,
1953
Earlier work this paper cites.
G. Källén and A. Sabry, “Fourth order vacuum polarization”,
1955
Earlier work this paper cites.
R.E. Cutkosky, “Some applications of the generalized unitarity relation,”
1960
Earlier work this paper cites.
C. Domb, “On the theory of cooperative phenomena in crystals,”
1960
Earlier work this paper cites.
A. Sabry, “Fourth order spectral functions for the electron propagator”,
1962
Earlier work this paper cites.
I. Mannari and C. Kawabata, “Extend Watson integrals and their derivatives,”
1964
Earlier work this paper cites.
M. Abramowitz and I.A. Stegun,
1965
Earlier work this paper cites.
Gabriel Barton,
1965
Earlier work this paper cites.
G.S. Joyce, “Lattice Green function for the anisotropic face centred cubic lattice,”
1971
Earlier work this paper cites.
G.S. Joyce, “Exact evaluation of the body centred cubic lattice Green function,”
1971
Earlier work this paper cites.
G. Källén,
1972
Earlier work this paper cites.
G.S. Joyce, “On the simple cubic lattice Green function,”
1973
Earlier work this paper cites.
H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,”
1974
Earlier work this paper cites.
P. Barrucand, “A combinatorial identity,” Problem 75-4,
1975
Earlier work this paper cites.
M.L. Glasser, “Definite integrals of the complete elliptic integral
1976
Cited alongside, same era.
Kendall E. Atkinson,
1978
Cited alongside, same era.
L. Lewin
1981
Cited alongside, same era.
Yung-Li Wang, Chris Wentworth and B. Westwanski, “Linked-cluster expansion for quantum spin systems and the perpendicular susceptibility of the Ising model,”
1985
Cited alongside, same era.
A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev,
1986
Cited alongside, same era.
Jonathan M. Borwein and Peter B. Borwein,
1987
Cited alongside, same era.
Gert Almkvist and Bruce Berndt, “Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses,
S. Laporta, “High precision calculation of multiloop Feynman integrals by difference equations,”
2000
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David H. Bailey and David J. Broadhurst, “Parallel integer relation detection: techniques and applications,”
2001
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David H. Bailey, Yozo Hida, Xiaoye S. Li and Brandon Thompson, “ARPREC: An Arbitrary Precision Computation Package,” 2002,
2002
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D. Cvetkovic, P. Fowler, P. Rowlinson and D. Stevanovic, “Constructing fullerene graphs from eigenvalues and angles,”
2002
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S. Laporta, “High precision epsilon expansions of massive four loop vacuum bubbles,”
2002
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1988
Cited alongside, same era.
D.J. Broadhurst, “The master two-loop diagram with masses”,
1990
Cited alongside, same era.
F. Oberhettinger,
1990
Cited alongside, same era.
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
Cited alongside, same era.
A.I. Davydychev and J.B. Tausk, “Two-loop self-energy diagrams with different masses and the momentum expansion,”
1993
Cited alongside, same era.
A.J. Guttmann and T. Prellberg, “Staircase polygons, elliptic integrals, Heun functions and lattice Green functions,”
1993
Cited alongside, same era.
S. Groote, “Lectures on configuration space methods for sunrise type diagrams,” International Research Workshop on Calculations for Modern and Future Colliders (CALC 2003),
2003
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Jonathan M. Borwein, David H. Bailey and Roland Girgensohn,
2004
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A.I. Davydychev and R. Delbourgo, “Explicitly symmetrical treatment of three body phase space,”
2004
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G.S. Joyce and I.J. Zucker, “On the evaluation of generalized Watson integrals,”
2004
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David H. Bailey, Xiaoye S. Li and Karthik Jeyabalan, “A comparison of three high-precision quadrature schemes,”
2005
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Stéphane Ouvry, “Random Aharonov-Bohm vortices and some exactly solvable families of integrals,”
2005
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David H. Bailey and Jonathan M. Borwein, “Highly parallel, high-precision numerical integration,” manuscript, Jun 2006; LBNL-57491,
2006
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David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Integrals of the Ising class,”
2006
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R.S. Hijjawi, “Lattice Green’s function for the diamond lattice,”
2006
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D. Bailey, J. Borwein, N. Calkin, R. Girgensohn, R. Luke, and V. Moll,
2007
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David H. Bailey, David Borwein, Jonathan M. Borwein and Richard Crandall, “Hypergeometric forms for Ising-class integrals,”
2007
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David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Box integrals”,
2007
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V. Bârsan, “A two-parameter generalization of the complete elliptic integral of the second kind,” preprint, 2007,
2007
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Jonathan Borwein and Bruno Salvy, “A proof of a recursion for Bessel moments,” D-drive Preprint 346, 2007,
2007
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M.L. Glasser, “A two-parameter generalization of the complete elliptic integral of the second kind,”
2007
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S. Groote, J.G. Korner and A.A. Pivovarov, “On the evaluation of a certain class of Feynman diagrams in x- space: Sunrise-type topologies at any loop order,”
2007
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C.G. Papadopoulos and M. Worek, “Multi-parton cross sections at hadron colliders,”
2007
Later among the works it cites.
Jonathan M. Borwein and David H. Bailey,
2008
Closest in time.