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A245293
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Decimal expansion of the Landau-Kolmogorov constant C(4,1) for derivatives in the case L_infinity(infinity, infinity).
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0
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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
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OFFSET
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1,3
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COMMENTS
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.
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LINKS
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FORMULA
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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).
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EXAMPLE
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1.0809601238456275151880801506365456492375770747255234380135664425927599...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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