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A245293 Decimal expansion of the Landau-Kolmogorov constant C(4,1) for derivatives in the case L_infinity(infinity, infinity). 0
1, 0, 8, 0, 9, 6, 0, 1, 2, 3, 8, 4, 5, 6, 2, 7, 5, 1, 5, 1, 8, 8, 0, 8, 0, 1, 5, 0, 6, 3, 6, 5, 4, 5, 6, 4, 9, 2, 3, 7, 5, 7, 7, 0, 7, 4, 7, 2, 5, 5, 2, 3, 4, 3, 8, 0, 1, 3, 5, 6, 6, 4, 4, 2, 5, 9, 2, 7, 5, 9, 9, 0, 9, 7, 9, 0, 6, 6, 8, 5, 7, 2, 5, 0, 6, 8, 4, 8, 1, 8, 1, 1, 2, 7, 0, 7, 0, 7, 6, 1, 6, 1, 7, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
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(4,1) = 4*(2/3)^(1/4)/5^(3/4) = (512/375)^(1/4).

EXAMPLE

1.0809601238456275151880801506365456492375770747255234380135664425927599...

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[4, 1], 10, 105] // First

CROSSREFS

Cf. A050970, A050971, A244091, A245198.

Sequence in context: A254178 A154803 A166529 * A200018 A019937 A176460

Adjacent sequences:  A245290 A245291 A245292 * A245294 A245295 A245296

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jul 17 2014

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)