A074457 Consider surface area of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the best d.

7, 2, 5, 6, 9, 4, 6, 4, 0, 4, 8, 6, 0, 5, 7, 6, 7, 8, 0, 1, 3, 2, 8, 3, 8, 3, 8, 8, 6, 9, 0, 7, 6, 9, 2, 3, 6, 6, 1, 9, 0, 1, 7, 2, 3, 7, 1, 8, 3, 2, 1, 4, 8, 5, 7, 5, 0, 9, 8, 7, 9, 6, 7, 8, 7, 7, 7, 1, 0, 9, 3, 4, 6, 7, 3, 6, 8, 2, 0, 2, 7, 2, 8, 1, 7, 7, 2, 0, 2, 3, 8, 4, 8, 9, 7, 9, 2, 4, 6, 9, 2, 6

Offset: 1

Author

Robert G. Wilson v, Aug 22 2002

Keywords

• cons
• nonn

Examples

			7.256946404860576780132838388690769236619017237183214857509879678777...
		

References

• Nenad Cakic, Dusko Letic, and Branko Davidovic, The Hyperspherical functions of a derivative, Abstr. Appl. Anal. (2010) 364292 doi:10.1155/2010/364292
• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.

Links

• Dusko Letic, Nenad Cakic, Branko Davidovic, and Ivana Berkovic, Orthogonal and diagonal dimension fluxes of hyperspherical function, Advances in Difference Equations 2012, 2012:22. - From _N. J. A. Sloane_, Sep 04 2012
• Eric Weisstein's World of Mathematics, Hypersphere.

Crossrefs

Surface area is A074456. Cf. A072478, A072479, A074455.

Programs

Mathematica

RealDigits[ FindMinimum[ -n*Pi^(n/2)/(n/2)!, {n, 7}, WorkingPrecision -> 125] [[2, 1, 2]]] [[1]]
x /. FindRoot[ PolyGamma[x/2] == Log[Pi], {x, 7}, WorkingPrecision -> 105] // RealDigits // First (* Jean-François Alcover, Mar 28 2013 *)

Formula

Equals 2 + A074455.

Extensions

Corrected by Eric W. Weisstein, Aug 31 2003

Corrected by Martin Fuller, Jul 12 2007