A074457 - OEIS

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..102.

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.

FORMULA

Equals 2 + A074455.

EXAMPLE

7.256946404860576780132838388690769236619017237183214857509879678777...

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 *)

CROSSREFS

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

Sequence in context: A066903 A194886 A196764 * A200237 A072761 A337357

Adjacent sequences: A074454 A074455 A074456 * A074458 A074459 A074460