Experimental mathematics and mathematical physics. (English) Zbl 1221.82006

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim

Amdeberhan, Tewodros (ed.) et al., Gems in experimental mathematics. AMS special session on experimental mathematics, Washington, DC, January 5, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4869-2/pbk). Contemporary Mathematics 517, 41-58 (2010).

Summary: 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. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
For the entire collection see [Zbl 1193.00060].

MSC:

82-08	Computational methods (statistical mechanics) (MSC2010)
65D30	Numerical integration
82-04	Software, source code, etc. for problems pertaining to statistical mechanics
65Y04	Numerical algorithms for computer arithmetic, etc.

Keywords:

multi-dimensional integrals; Ising integrals; box integrals; Clausen functions; multiple zeta values; Euler sums; high accuracy