Fetching the paper…
Reading the bibliography…
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values.
S. Smolyak, “Quadrature and interpolation formulas for tensor products of certain classes of functions,” Soviet Math. Dokl. , vol. 4 (1963), 240243
1963
Earlier work this paper cites.
P. Barrucand, “Sur la somme des puissances des coefficients multinomiaux et les puissances successives d’une fonction de Bessel,” Comptes rendus hebdomadaires des séances de l’Académie des sciences , vol. 258 (1964), 5318–5320
1964
Earlier work this paper cites.
Milton Abramowitz and Irene A. Stegun, ed., Handbook of Mathematical Functions , Dover, New York, 1972
1972
Earlier work this paper cites.
H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publications of RIMS , Kyoto University, vol. 9 (1974), pg. 721–741
1974
Earlier work this paper cites.
R. Anderssen, R. Brent, D. Daley, and P. Moran, “Concerning ∫ 0 1 ⋯ ∫ 0 1 ( x 1 2 + ⋯ x n 2 ) 1 2 d x 1 ⋯ d x n \int_{0}^{1}\cdots\int_{0}^{1}(x_{1}^{2}+\cdots x_{n}^{2})^{\frac{1}{2}}\ dx_{1}\cdots dx_{n} and a Taylor series method,” SIAM Journal of Applied Mathematics , vol. 30 (1976), 22–30
1976
Earlier work this paper cites.
A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring Polynomials with Rational Coefficients
1982
Earlier work this paper cites.
D. Zagier, “Hyperbolic manifolds and special values of Dedekind zeta-functions,” Invent. Math. , vol. 83 (1986), 285–301
1986
Earlier work this paper cites.
D. Zagier,“The remarkable dilogarithm,” J. Math. Phys. Sci
1988
Earlier work this paper cites.
T. Ooura and M. Mori, “Double exponential formulas for oscillatory functions over the half infinite interval,” Journal of Computational and Applied Mathematics , vol. 38 (1991), 353–360
1991
Earlier work this paper cites.
D. Zagier, “Polylogarithms, Dedekind zeta functions and the algebraic K K -theory of fields,” in: Arithmetic algebraic geometry
1991
Earlier work this paper cites.
C. Zenger, “Sparse grids,” in W. Hackbusch, ed., Parallel Algorithms for Partial Differential Equations , vol. 31 of Notes on Numerical Fluid Mechanics , Vieweg, 1991
1991
Earlier work this paper cites.
Kendall E. Atkinson, Elementary Numerical Analysis , John Wiley, 1993
1993
Cited alongside, same era.
D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
1997
Cited alongside, same era.
J. M. Borwein and D. J. Broadhurst, “Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links,” [arXiv:hep-th/9811173]
1998
Cited alongside, same era.
Wolfram Koepf, Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities , American Mathematical Society, Providence, RI, 1998
1998
Cited alongside, same era.
Michael Trott, “The area of a random triangle,” Mathematica Journal , vol. 7 (1998), 189–198
1998
Cited alongside, same era.
Michael Trott, Private communication, 2005
2005
Later among the works it cites.
David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Integrals of the Ising class,” Journal of Physics A: Mathematics and General , vol. 39 (2006), 12271–12302
2006
Later among the works it cites.
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, and Eric W. Weisstein, “Ten problems in experimental mathematics,” American Mathematical Monthly , vol. 113 (2006), 481–509
2006
Later among the works it cites.
David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Box integrals,” Journal of Computational and Applied Mathematics , vol. 206 (2007), 196–208
2007
Later among the works it cites.
David H. Bailey, David Borwein, Jonathan M. Borwein and Richard Crandall, “Hypergeometric forms for Ising-class integrals,” Experimental Mathematics , vol. 16 (2007), no. 3, 257–276
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Helaman R. P. Ferguson, David H. Bailey and Stephen Arno, “Analysis of PSLQ, an integer relation finding algorithm,” Mathematics of Computation , vol. 68, no. 225 (Jan 1999), 351–369
1999
Cited alongside, same era.
D. H. Bailey and D. Broadhurst, “Parallel integer relation detection: Techniques and applications,” Mathematics of Computation , vol. 70, no. 236 (2000), 1719–1736
2000
Cited alongside, same era.
H. Boos and V. Korepin, “Evaluation of integrals representing correlations in the X X X XXX Heisenberg spin chain,” in: MathPhys Odyssey, 2001
2002
Cited alongside, same era.
Jonathan M. Borwein, David H. Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Routes to Discovery , A. K. Peters, Natick, MA, 2004
2004
Cited alongside, same era.
D. H. Bailey, X. S. Li and K. Jeyabalan, “A comparison of three high-precision quadrature schemes,” Experimental Mathematics , vol. 14 (2005), 317–329
2005
Cited alongside, same era.
David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, “Advances in the Theory of Box Integrals,” to appear in Mathematics of Computation ; available at http://crd.lbl.gov/
Cited in the paper.
J. Blümlein, D. J. Broadhurst and J. A. M. Vermaseren, The Multiple Zeta Value Data Mine
Cited in the paper.
2007
Later among the works it cites.
David H. Bailey, Jonathan M. Borwein, Neil Calkin, Roland Girgensohn, Russell Luke and Victor Moll, Experimental Mathematics in Action , A. K. Peters, Wellesley, MA, 2007
2007
Later among the works it cites.
David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, “Elliptic integral evaluations of Bessel moments,” Journal of Physics A: Mathematics and General , vol. 41 (2008), 205203
2008
Later among the works it cites.
Jonathan M. Borwein and David H. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century , A. K. Peters, Natick, MA, second edition, 2008
2008
Later among the works it cites.
Jonathan M. Borwein and Bruno Salvy, “A proof of a recursion for Bessel moments,” Experimental Mathematics , vol. 17 (2008), 223–230
2008
Later among the works it cites.
2008
Later among the works it cites.