A244337 - OEIS

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A244337

Decimal expansion of the upper bound of the 5-dimensional simultaneous Diophantine approximation constant.

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

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OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.23 Diophantine Approximation Constants, p. 174.

LINKS

Table of n, a(n) for n=0..102.

W. G. Spohn, Blichfeldt's Theorem and Simultaneous Diophantine Approximation

Eric Weisstein's MathWorld, Blichfeldt's Theorem

FORMULA

1/(k*2^(k+1)*integral_(0..1) x^(k-1)/((x^k+1)*(x+1)^k) dx = 3/(208 + 72*Pi - 96*sqrt(2)*Pi), with k = 4.

EXAMPLE