A245296 Decimal expansion of the Landau-Kolmogorov constant C(5,1) for derivatives in the case L_infinity(infinity, infinity).

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

Offset

1,3

Comments

See A245198.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's MathWorld, Landau-Kolmogorov Constants

Eric Weisstein's MathWorld, Favard Constants

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).

C(5,1) = (5*5^(4/5))/(8*2^(4/5)*3^(1/5)) = (1953125/1572864)^(1/5).

Example

1.0442579093097951434453696171557025830804208042025372077576134158002325888...

Mathematica

a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5, 1], 10, 105] // First

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Sequence in context: A339703 A300844 A011321 * A273616 A064860 A091223

Adjacent sequences: A245293 A245294 A245295 * A245297 A245298 A245299

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 17 2014

Status

approved