Box Integral

A box integral for dimension n with parameters q and s is defined as the expectation of distance from a fixed point q of a point r chosen at random over the unit n-cube,


(Bailey et al. 2006).

Two special cases include


which, with s=1, correspond to hypercube point picking (to a fixed vertex) and hypercube line picking, respectively.

Hypercube point picking to the center is given by


See also

Hypercube Line Picking, Hypercube Point Picking, Unit Cube, Unit Square, Unit Square Integral

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Bailey, D. H.; Borwein, J. M.; and Crandall, R. E. "Box Integrals." Preprint. Apr. 3, 2006.Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 238 and 272, 2007.

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Box Integral

Cite this as:

Weisstein, Eric W. "Box Integral." From MathWorld--A Wolfram Web Resource.

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